Necessary for an explanation does not, itself, make them real of non-illusory, though. It only makes the concept, as understood at the time, useful in that context.
Whether time is an illusion or not is a question that is not so simply dismissed out of personal incredulity.

To wit, some articles discussing the matter, from the first page of a Google on the subject:
https://www.nature.com/articles/d41586-018-04558-7
https://www.scientificamerican.com/article/is-time-an-illusion/
https://www.npr.org/2022/12/16/1139780043/what-is-time-physics-atomic-clocks-society
https://www.space.com/29859-the-illusion-of-time.html
How it relates to broken watches, though, which utilise the current mainstream view of a passing time, I can not say. Nor to an "infinite time", as far as I can tell, as whether time passes or happens all at once, doesn't alter how much of it there is?
Anyhoo, maybe the OP will clarify the issue they want to discuss here?