After playing through the current version thoroughly, here's my thoughts on the present situation.
1. The early-game damage is way too high: it's difficult if not impossible in some cases to lay an early-game siege due to city damage. This certainly makes Authority less fun.
2. Late-game generally seems OK in most situations. Actually if anything, I found that my advanced units weren't taking much to any damage at all (but perhaps that's because I'm quite advanced in tech).
I was thinking of a more boring and straight-forward solution.
What if cities just did 30 damage? Period. It's a good number that yields eventual results. It won't autokill things. This number applies regardless of City Strength.
The only things that would modify the damage are the ranged defence promotion, and city % damage increases (e.g. from God of War). This way you know there is always a real threat at all times and you can't pretend like there isn't, but it's not so strong that your units will simply vanish from the battlefield.