Hello, Ellipticmodulo, and welcome to the Grammar Exchange.

David, our moderator, provided a very thorough answer to a similar question here some time ago.

It is true that "why to" is much more limited in use than other "wh"-word + to infinitive constructions. In fact, your sentence:

No one knew why to cancel the swimming class.

sounds wrong.

"why" + to infinitive will be much more usual in titles:

Why to cancel the swimming class (= Reasons for canceling the swimming class):

- Because the swimming coach or the lifeguard are absent.
- Because the water is too cold.
- Because there are too few participants.

Instead, "why" followed by a bare infinitive is usual in full sentences, being short for a longer question in which the auxiliary and the subject have been ellided:

Why cancel the swimming class if everyone wants to take it? (Why should we cancel the swimming class ...?)

Apart from the example David provided towards the end of that other thread I quoted, here is another one I found on the Internet:

There’s no real need to explain why to go here. Everything people say about it is true. Great food, amazing museums, ancient buildings, small streets, and awesome gelato. (Source: https://dstravelguide.wordpress.com/2017/12/10/italy/)

It also seems to me that, unlike other "wh"- words, "why" has some time restrictions (the reason expressed by the infinitive and the main verb usually need to be contemporary). Thus, while we can have:

- No one knows (now) where/how to go tomorrow. 
- No one knew (yesterday) who to ask today.
- No one knows (now) what to do tomorrow.
- We have not yet decided when to go swimming.

"why" seems to be only suitable with certain verbs and tenses to convey simultaneity:

- You should explain to him (now) why to quit smoking (why it is advisable for him to quit smoking).
- There’s no real need to explain why to go here. (It isn't really necessary to explain why going there is a must.)

While the "to"- infinitive can express futurity with most "wh"- words, it cannot with "why," and this makes this combination the least productive.

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