If I need a new pair of glasses with the same prescription I have now (Say, for example, I fall and break my glasses), I shouldn't be required to go get examined to get a new pair simply because it has been more than a year. I want the same thing I've been wearing, and the worst possible outcome from me getting them is that (if my prescription has worsened, which it hasn't in 4+ years) I can't see quite as clearly at long range as I ought to.

That would be weird, good thing you are not required to get examined in order to buy glasses. I don't know why you think you are required.

You are required to get a new prescription because your original prescription expired.

It's by state.

Not for contact lenses (16 CFR 315.5):

https://www.law.cornell.edu/cfr/text/16/315.5

That doesn't make much sense because adult vision doesn't change much. It should be perfectly valid to use an old prescription unless you want to re-check your vision. I've never seen this law in Asia or Europe and people are living just fine.

I just had an eye test and both of my eyes had changed enough after two years to make a very noticable difference to my prescription.