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?

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.