Frame challenge: summon lesser demons and summon greater demon won’t work either.
If you are looking for a way for the same wizard to cast planar binding on a creature that it has conjured or summoned, it may be harder than you think. A spell that conjures or summons a creature typically requires concentration. Conjure elemental, summon lesser demons, summon greater demon, conjure celestial and conjure fey all do.
For most of these spells, one spellcaster would have to cast the spell to conjure or summon the creature, and maintain concentration on it while a second spellcaster casts planar binding. This is because planar binding has a casting time of 1 hour, and when a spell has a casting time of longer than 1 action, the caster has to use concentration throughout the casting (Player’s Handbook p. 202), so they cannot concentrate on another spell at the same time.
Even if conjure celestial were on the wizard spell list, you would run into this issue. You also run into this issue with the new summoning spells from Tasha’s Cauldron of Everything.
However, this could work with conjure elemental.
A wizard can cast conjure elemental, trap it inside a 4th-level or higher magic circle that had previously been cast, drop concentration, and the elemental won’t disappear for an hour. The wizard can then immediately cast planar binding on it. (A 3rd-level magic circle would likely disappear before the planar binding casting was complete.)
This would also work for conjure fey if it were on the wizard spell list.