To me, these
He'll come, if he wants
He'll come, if he's able
He'll come, if I allow him
are simply variants of
He'll come, if he wants to
He'll come, if he's able to
He'll come, if I allow him to
in other words, the infinitive marker "to" is optional; it's omitted simply because it can be omitted. But this is instinct on my part; some people tell me that "to" is required, and omitting it makes the sentences unacceptable (if not ungrammatical).
Grammatically speaking, is "to" in the above sentences required or optional? And what's the linguistic/grammatical case for it?
(By the way, is this a case of "preposition stranding" or does it go by another name in the literature?)
Thanks in advance
edit: It's been pointed out that this question is a possible duplicate of another question, but that question focuses on whether the to-infinitive or the bare infinitive is used after the verb "help." My question focuses on the infinitive marker "to" and what dictates/allows its omission when the infinitive itself has already been omitted. So, for example, instead of saying "He'll come, if he wants to come," is "He'll come, if he wants" acceptable or is one grammatically required to say "He'll come, if he wants to."