[tep]

Normalization wouldn't help as the problem is compression. If A has a very narrow dynamic range (because it is heavily compressed) and B a rather broad one - think metal band vs orchestra - then after normalization A would still sound much louder than B.

This is because only the loudest signal hits 0db then. If a signal is on average mainly quiet, it will stay quiet. And if it is pretty loud, it will stay loud.