You say you don't want to replace attack rolls with save throws, but you keep putting an equal-sign between them.
The biggest difference that comes to mind is that one is a magical exploding ball of fire, the other is a pointy stick. It's easy for me to understand why damage might be inescapable when a room is exploding along with everything in it. But when you're jabbing at someone with an ordinary pointy stick, its quite easy for me to see how they might, you know...miss. Completely. As in, not make contact with anything, not force a response from their target, and not impress anyone who might be watching.
Some people in this thread clearly see it differently. I can't really speak to that; all I can say about it is that weapon damage on a miss doesn't really make sense to me. So I won't use it.