We were always supposed to put punctuation inside quotation marks;

Isn't this a US English thing? In India we were taught to close them like brackets - i.e., the one that opened last closes first. So

'Don't wait. I will come later.'

But

He said 'I will come later'.

Yeah, I still feel like I'm supposed to, but frequently I think it makes more sense to pull it outside if it isn't part of the quote. Putting it in the quotation makes it seem like it's associated with the quotation, when it may not be.

You know, I actually prefer that it be variable, but only when it serves a purpose.

Like, if Im quoting someone "I might want to indicate that they completed a sentence.", but also continue beyond it.

For me, i make peace with this by thinking, the rules are one way for writing dialog, and perhaps another way when needing to convey the exactness of a quote.