Is there no way for a lone caster to planar bind a demon/devil with the Xanathar's spells?

I refer specifically to the spells infernal calling and summon greater demon. Unlike the conjure elemental and conjure fey spells, which cause the monster to stay for the rest of the duration when you drop concentration rather than disappearing, which gives you just enough time to attempt to planar bind, the new spells cause the Devil and Demon to disappear within a few seconds to minutes as soon as you drop concentration, and you have no way to keep them there.

The only thing a conjuration wizard can bind in 5e are elementals until they get gate, unless they get help from another caster to summon the monster they want for them, which goes against the normally insular attitude of wizards, and doesn't make a lot of sense to me.

Am I missing something or is this basically the only solution besides going to a plane with the creature you want and trying to capture one there?

You can use the Glyph of Warding (p. 245 PHB) to store Planar Binding (p. 265 PHB) and/or Magic Circle (p. 256 PHB) in order to bind "a celestial, an elemental. a fey. or a fiend to your service." Cast either Infernal Calling or Summon Greater Demon on top of the glyph to trigger it.

A spell glyph can be inscribed on any surface. It can store any spell of the Glyph's spell level or lower which targets a single creature (Planar Binding) or an area (Magic Circle), or which summons hostile creatures or traps (specifically used as an example in the spell). If the target of the Planar Binding ward fails their save, they are bound. When the Glyph is triggered, the stored spell is cast. Concentration spells last their full duration regardless, as explicitly stated under the "Spell Glyph" entry.

There is little question either RAW or RAI whether a Glyph can be used in this way. This would allow a single mage to planar bind summoned creatures given time and resources.

To do this:

1. Cast Glyph of Warding - Spell Glyph to store a casting of Planar Binding.


2. Cast Glyph of Warding - Spell Glyph to store a casting of Magic Circle for safety.


3. 
   

   Cast Summon Greater Demon/Infernal Calling either right on top of the glyphs or outside the glyphs (later commanding them to give their true name and walk onto the glyphs)

   
   
   

   Optional: Cast Feeblemind on the demon/devil to tank its Charisma saving throw to guarantee success.

   
   

Also, Planar Binding reads "The creature must be within range for the entire casting of the spell." This could be interpreted to mean that you cannot planar bind via a Glyph, but there is a way around this problem.

• Cast Glyph of Warding - Spell Glyph to store Summon Greater Demon (Summons are expressly allowed to be stored within the Glyph's text) and set the spell to trigger on a command word.


• Cast Glyph of Warding - Spell Glyph to store Magic Circle for safety and set it to trigger once a demon enters the area.


• Trigger the first glyph with your verbal command. It doesn't matter if you don't control the demon - the Magic Circle will contain it regardless. Immediately cast Planar Binding to bind the demon.

If timing is STILL deemed to be an issue for your DM (the summon lasts 1 hour and Planar Binding has a 1 hour cast time), 2 levels of Sorcerer can snag you the Extended Spell metamagic to prolong the summoning to allow you to bind the demon.

This trick also works with Gate. Use Gate to summon a powerful celestial, elemental, fey, or fiend (preferably something without legendary resistances - something like a Red Abishai or a Goristro, for example). Magic Circle can prevent them from leaving the plane unless they pass a Cha check. Slap them with Feeblemind to tank their saving throws and hard-cast Planar Binding.

ALTERNATE 2: Use a Simulacrum at level 13 to assist you.

There is no way for a lone wizard to bind fiends summoned from those spells specifically, depending on the interaction with magic circle

Infernal calling (XGtE, p. 158) says:

The devil disappears ... when the spell ends.

[...]

If your concentration ends before the spell reaches its full duration, the devil doesn't disappear if it has become immune to your verbal commands. Instead, it acts in whatever manner it chooses for 3d6 minutes, and then it disappears.

So when your concentration drops, it either disappears (if you still had control) or it stays for 3d6 minutes, then disappears.

Summon greater demon (XGtE, pp. 166-167) says:

... the demon disappears ... when the spell ends.

[...]

If you stop concentrating on the spell before it reaches its full duration, an uncontrolled demon doesn't disappear for 1d6 rounds if it still has hit points.

Similar to infernal calling, it either disappears at the end of the spell, or it hanges around for 1d6 minutes, then disappears.

Magic circle (PHB, pp. 256-257) says:

The circle affects a creature of the chosen type in the following ways:

• The creature can't willing enter the cylinder by nonmagical means. If the creatures tries to use teleportation or interplanar travel to do so, it must first succeed on a Charisma saving throw.
  

[...]

When you cast this spell, you can elect to cause its magic to operate in the reverse direction, preventing a creature of the specified type from leaving the cylinder ...

This is where it becomes a bit unclear; the fiend was summoned by your spell, and it isn't necessarily leaving the inverted magic circle using its own magic. Does that mean you have to make the Charisma saving throw? This might be down to the DM to adjudicate:

• if it can't leave (i.e. if it still needs to make the Charisma saving throw to return to its native plane, even though you were the one who summoned it here), then assuming it fails the save, you don't need to maintain concentration on it, and the planar binding spell can then be used on the now-bound fiend.


• if it can leave because the DM decides that it isn't trying to teleport away, but rather your summoning spell is just resolving itself, then the demon will disappear before you can complete the casting of planar binding (more on this below).

In the PHB (p. 202), under "Longer Casting Times", it says:

When you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn casting the spell, and you must maintain your concentration while you do so ...

Therefore, it is clear that you cannot concentrate on the summoning spells and the planar binding spell. As soon as you start casting planar binding, your concentration on either infernal calling or summon greater demon will end, and as per their spell descriptions (assuming the second listed interpretation of magic circle, see bullet points above) they will either disappear immediately or they will hang around for a few rounds before disappearing; this is not long enough to complete the planar binding spell, so it will fail, unless a ruling about magic circle keeps the fiend in place.

Rules as written, I don't think there is a way a single caster can contain, summon, and planar bind an entity

My understanding is as follows:

• A spell with casting time of more than an action, bonus action or reaction requires concentration to be cast successfully




• Planar binding takes an hour to cast (and this requires concentration)




• Summoning most extra-planar creatures requires concentration, after which they will vanish (either immediately or a couple rounda after)

Sources:

Longer Casting Times

Certain spells (including spells cast as rituals) require more time to cast: minutes or even hours. When you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn casting the spell, and you must maintain your concentration while you do so (see "Concentration" below). If your concentration is broken, the spell fails, but you don't expend a spell slot. If you want to try casting the spell again, you must start over. (PHB 202)

Planar Binding

Summon Greater Demon is a concentration spell of up to 1 hour.

Note: this is dependent on how the spell Magic Circle works. If magic circle keeps a summoned creature within the "reversed" form of the spell even when concentration ends, then this may work. However, it is not clear what the interaction between the two are.

Use Glyph of Warding

While wizards generally can get around this problem by working with other wizards, nevertheless an unusually hermetic wizard need not want of the services bound demons can provide.

The obstacles to using planar binding on a creature summoned via, e.g., summon greater demon are that planar binding has a casting time that may conflict with the maximum duration of the summoning spell and that summoning spells generally require concentration while in use yet planar binding requires concentration while being cast. Glyph of Warding eliminates both potential problems, even for an atypically anticollegic wizard, provided they are willing and able to acquire the necessary expensive material components for each casting.

Glyph of Warding takes an hour to cast, during which you may store any prepared spell up to a certain level within it, within certain targetting restrictions planar binding complies with. Once you have stored planar binding within a spell glyph, you can freely summon and bind any compatible creature you'd like; the glyph can be set to trigger as soon as the summoned creature appears.

Note that, because you never get two 9th level spell slots as a Wizard (barring access to super-useful magic items like the Tome of the Stilled Tongue that seem to all be tied to wizards working as a group and thus likely off-limits for our self-imposed-exile wizard) you will be limited when using this method to a planar binding spell that is one level below the highest you can cast from 11th level onwards barring rest timing shenanigans.