In a way they go up because they can. If you look at it from their point of view. It is an event which they can point to and justify and say "sorry, this is our policy" and just raise the rates.
Now of course if they charge too high, then you could go to a competitor. But there is this CLUE database (I just learned about in a sibling comment here) which apparently is shared among insurers and depending on what is there (or what is not there! -- such as, it was really just an accident) you get labeled and dropped. So even a competitor might decide it is safe to stay away from you.
