It's not the punishment but the likelihood of being punished.

Even if the punishment is not that severe, a high probability of being caught is a much greater deterrent.

Honestly, that sounds plausible, but how would you achieve higher conviction rates?

You're not going to get far with the current US police. If you compare the money put in to the crime stats, the picture is one of an extreme inefficiency. They've failed in their mission to such an extent that a large minority of people simply don't trust them enough for them to do their duty to those people. They've preside over a third-world crime rate with first world tax revenues.

At this point, it would be reasonable to start talking about a wholesale reboot of the whole operation.

However, if that's too radical, or too expensive, it would seem pragmatic to try and target crime through some other mechanism - e.g. welfare.