And, even within a town, it's not unusual for streets to change name a couple times in the course of a few miles. And towns reuse street names all the time--especially for things like Main Street.
You say that as if it was a bad thing. This idea that a "street" is a line on the map, and whether there is actually asphalt at that spot is yet to be defined -- this is a very strange idea to me. If I get to the right street, I expect to be able to follow it until I get to the correct address. Streets with gaps in them don't work so well for this.
Yes, if the city is laid out in a rectangular grid, that has its advantags, too. But I just want to point out a different way to look at things.
(European perspective.)
Assuming you're on the street in the correct town, sure.
Continuity is actually one of the things that was fixed as part of the whole E911 system in the US. Before that, you would sometimes have streets that, for example, would have two segments that weren't actually connected in the middle. Or you'd have a single named road with a T shape or some other layout that meant you couldn't just follow it from one end to the other.
You also, as someone else mentioned, used to have houses with rural route numbers (I grew up on one) that didn't have a street address at all. In our case, our town address didn't even correspond to where we were located because it was the adjacent town that did the RR deliveries.
Seemed strange to me that Rambus could be in Los Altos (a largely residential town) until I drove past it one day and thought it was in Mountain View.