I don't "dislike the word bad". It simply does not apply here and is semantically different from "worse than". One is relative and the other (subjectively) absolute.

Getting hit on the foot with a sledgehammer is bad for you. But it's better than getting hit in the head with a sledgehammer. Using "better than" here does not make the former good for you, however.

That's how language works. It is important to be precise, for earlier mentioned reasons.