I do this:

They may care about mortals, but almost never help them because "something something cosmic pacts and treaties", giving the impression that evil is allowed to run unchecked in the multiverse while Mount Celestia is lead by their equivalent of Neville Chamberlain.

...because this:

I can also see how it may be hard to try using Celestials in a capacity that doesn't put them in a deus ex machina situation. PCs should be the main stars of the story, not powerful outsiders. So naturally it may just be easier to depict them as villains, or otherwise oppose the party.

I appreciate your point, but I think that "almost never help them" is the right amount of help to preserve player agency. At best, if I as DM provide a resource to help a character overcome a challenge I am going to give them another challenge in exchange.

I absolutely put the Forces of Good in a 'long detente' with the Forces of Evil, because I want player characters to solve problems, and when PCs can't or don't want to solve problems, I'd rather the problem go unresolved than solve it for them.