why doesn't generic increased damage count towards minion damage?

To answer the original question, it doesn't affect minions because that's how the game works.

Onto discussion:

If generic damage nodes state they exclude minions, people will assume other nodes (like fire nodes) affect minions. No, the wording is consistent among all modifiers, and should remain this way.

Mechanically, nothing affects minions unless specifically stated otherwise. This is universally true. There is no need for clarification.

I would raise that it's fine to not change this. The only reason you've given for such a change is a minor inconsistency that only you seem to perceive. I'd say that is not enough reason for such a extensive change.

Should also count towards monsters imo.
Just using your logic.