Can someone explain why potty training works (not how)?

I'm trying to understand why potty training works.

So, when the puppy goes potty outside, you praise and treat (positive) which would make it like to go potty outside. That piece makes sense. When a puppy goes potty inside, you are supposed to *not* react, and just calmly clean up (neutral). I guess the rationale is that eventually, the puppy will not want to potty inside, because it would rather do it outside and get the treat. That seems surprising to me because dogs do all sorts of behaviors that don't result in treats. e.g. a dog may know that when you say "sit", it will get a treat for sitting, but that doesn't mean it will be reluctant to just sit other times, if it wont get a treat. So why would it not want to potty indoors?

And then eventually, after lots of training, the puppy will start whining when it needs to go potty and "ask" to be let out. So, is it whining because it knows that if it goes potty inside it wont get the treat for doing it outside? Dogs don't usually whine if they know that they are about to do a behavior that wont result in treats, so why here?

I know that also puppies don't want to go potty in their crate, and part of it maybe that eventually they learn that your house is "home" and not a place to go to the bathroom. But what about other people's houses and other indoor places?

I feel like I'm missing something about the behavioral science here?