OK so there are a couple of things:

The congregation needs to have a reasonable expectation of what to expect at a given Mass, because the church currently puts a premium on congregational participation for all/most/much of the Ordinary. So singing whatever one feels like with no rhyme or reason, that can change from one week to the next and not just one occasion or season to the next, is unreasonable. It’s also a lot of work to prepare.

Each season and feast has a different character, or related characters, and the tradition is to change between Gregorian settings as a result. now, the listing in the modern editions of chant books isn’t fixed, except that one usually wouldn’t use the ferial settings on Sundays or feasts, and one had to use the penitential ferial setting on those days which call for it, but one could have some flexibility otherwise. This applies to modern settings no matter the language and even to polyphony. The bonus is that while there isn’t necessarily an upper fixed number or even a lower one to assure congregational participation, I think that doing a few settings more often helps them learn, and eventually you can add more (particularly chant settings). We also find that with chant people participate in some parts better than others even in settings that we do seasonally and have done for years and years.

I don’t think that this is the kind of thing for which there is official proof, because you could ignore what I said and impose one setting for every Mass (I know an Ordinariate community that, unless it was a Latin polyphonic setting, only did the Willan setting used by the Ordinariate as its default…)