I think this question, as it is actually phrased, deserves more attention.
Why not a bare infinitive?
Bare infinitives are licensed in a few cases. Offhand, I know that we use them along with modal auxiliaries, certain verbs of causation and perception, and sometimes with the verb "to help" (which happens to license both the bare and the full infinitive forms). We even use them on occasion to mark the subjunctive mode. There may be other cases that, as a native speaker, I'd find easy to recognize but hard to recall.
The verb "to be" doesn't fall under any of those cases. If we want an infinitive here, we'll need to use the full form.
Why not any infinitive?
Sure. Why not? Sometimes, it even works.
Is smoking to allow?
The sentence above is grammatically correct. Despite that, I still can't make sense of it. As it stands, it's a question that should accept both "yes, smoking does allow" and "no, smoking doesn't allow" as legitimate, complete answers. We have no object for the verb "to allow", and we have no context that lets "smoking" represent the kind of thing that allows something else.
Is the school to allow smoking?
The sentence above is also grammatically correct. Even more importantly, I can make sense of it. A school is the kind of thing that can allow something else, and the gerund "smoking" makes a suitable direct object for the verb "to allow".
We often use infinitives and infinitive phrases to represent things like intention, expectation and purpose. We can understand the question above to mean "does someone intend that the school allow smoking?" or "do we expect that the school will allow smoking?" or maybe even "is permission to smoke part of the purpose of this school?"
Those questions are, of course, quite different from "does the school allow smoking?"
Why does "does" do that?
Does the school allow smoking?
In this example, we do have a modal auxiliary: "does". The mode that this verb denotes is indicative, which is the reason that we can use it without changing the meaning of the clause. We commonly use it either to add emphasis or to form question exactly like the one above.
Thanks to "does", we have a reason to use the bare infinitive "allow" -- a reason that we don't have in the questions that start with "is". On the other hand, thanks to "allow", we have a reason to use "does". When forming questions we want the first word of the verb construction -- an auxiliary -- to come before the subject. When the verb construction lacks an auxiliary, forms of "do" come to our rescue.
Do we "do be" too?
The verb "to be" is a special case. It works well with other auxiliaries, but it doesn't work with the auxiliary "do". We can take a statement like "it is true" and change it to "it should be true", "it could be true" and so on. We can ask question like "should it be true?" and "could it be true?" However, we can't form "it does be true" and "does it be true?". Instead, we let "is it true?" stand as the natural form of the question, without a hint of do-support in sight.