I used to really spam doges before factions were introduced. They are amazing money generators. I don't use them at all right now, but maybe I'm too shy about this. I am concerned about how rebellious they are. I didn't used to mind because they're so easy to put down in a one-off revolt -- cities are easy to assault. But now that they can revolt and bring in an alien paratrooper 100k no-attrition doomstack, I avoid them. I don't want anyone who might revolt, not because I can't take them down but because I don't want to deal with the free doomstack.
The other problem with republics is they're only useful in same-culture areas. The mayors usually take on the culture of the county they're in. In big empires, this often means your base area only. Later, once culture spreads, you can revoke and make more. But by then, I usually have other targets for revoking that are more important.
I only use them in same culture areas. It's country dependent but for ERE -> Rome game replacing feudal vassals in starting Greek culture territory was more then enough. Other important factor is that they are weakest vassals in terms of military strength so it's not that easy for them to revolt and as my empire grows their relative strength is smaller and smaller.
Now in 1.08 it should be even easier as they won't join independence faction.