Not that my opinion on the law matters, but I'd say felony murder rules make a lot of sense in many scenarios. If you accidentally fatally knock a man to the ground while deliberately robbing him, that's felony murder even though the killing itself was accidental. After all, the robbery was no accident. Surely killing a man by accident while committing a felony is itself a heinous crime. Calling it manslaughter just doesn't cut it. Not in my book anyway.
It only gets weird when you have two or more criminals cooperating with each other. That's when you get scenarios where one of the criminals is lawfully killed (by the police or otherwise) and another is charged with felony murder. I don't have any statistics for it, but I suspect a more common scenario is one of the criminals commits 'traditional' murder and the other criminals are then charged with felony murder for their general participation. Without some sort of felony murder you might be able to get the other participants with some sort of "conspiracy to commit" type law, but maybe not.
A more serious criticism of felony murder laws is that it incentivizes killing more witnesses after one victim has been accidentally killed, particularly in states where capital punishment is on the table for felony murder. After all, if a criminal accidentally kills one victim and is now a candidate for execution, there is little incentive left for him to not deliberately murder any witnesses (under the theory that murdering witnesses lowers the probability of capture/conviction.) It's difficult to guess how many multiple-murders started out with an accidental killing that escalated in this manner. But I'd wager this has happened far more often than the scenario where a robber is charged with murder after the police gun down his partner.