Yes, and? It's a good thing to get crimes reported more often, faster, and with more and higher quality evidence. (That last statement doesn't directly follow from bounties in the short term, but it does once you start considering the competitive pressures crime detectors face in such a market.)

You can run a thought experiment to confirm this. Suppose 1/2 of all crimes committed in your area currently get reported. You are offered the option to move to two new places, identical in every way to your starting point, except New Town A has 3/4 of the crimes committed get reported*. New Town B has only 1/4 of the crimes committed get reported. Do you move? Where to?

The important thing to notice is less that New Town A seems like a pretty good deal, than that New Town B seems like a really bad one. Plenty of people would move to New Town A for the obvious additional security. Some of people would elect to stay, for reasons like New Town A isn't guaranteed to be exactly like where you currently are into the future, and home is home. But almost nobody would move to New Town B. The people who would jump for joy at moving to New Town B may even be criminals themselves trying to escape charges or just hedge their futures.

* For the sake of completeness, you can consider this property preserved across different types of crime. E.g. if 90% of homicides get reported in your current locale, 95% do in New Town A, and only 45% in New Town B do. If 20% of money laundering schemes get reported, 60% do in New Town A, and 10% in New Town B. Etc. The general idea of everything being more or less detectable is more important than the specific numbers.