Some things that would make Governors much more helpful:
1. An option to set the default specialist setting. While managing citizens moods, the Governors will only allow enough entertainers to keep the city from going into anarchy. I like to keep my people happy, so this doesn't allow me to have access to the nice things governors do, like put people back to work after pollution is cleaned up. As it is, the Governors seem to do the opposite of what I'd like with specialists. With my tax rate high, everyone becomes scientists, and with the tax rate low, everyone becomes a tax collector.
2. An option to disallow the Governors to change specialists. I like to set my specialists on a per city basis, but with Governors managing citizens moods, they change the specialists to what they want every single turn. Again this keeps me from being able to turn them on, and I have to manually reset workers who turn to specialists when pollution inevitably shows up. Having both option 1 and 2 would be nice, but either/or would do.
3. If 1 and 2 aren't feasible, then an option to keep working on polluted squares. I always clean up every pollution square every turn anyways, it's just annoying to have to go into the city screen and put the land back to use. If I had specifically set up a city to avoid the continual starvation loop, then it just adds more headaches trying to get it right again. Not only in the affected city, but often in surrounding cities with overlapping tiles as well.
4. Being able to give the Governors a build queue that every city should follow. Often in the late game all I want to build in a vast number of corrupt cities is an Aqueduct, Marketplace, Hospital, and Mass Transit, then switch to Wealth. I can set them all myself quite easily, but it does involve a lot of extra clicking. Especially on Large/Huge maps. Once an important city improvement becomes available, it would be nice to be able to instantly insert that into the build queue in every city.
5. Not really Governor related, but a late game issue. Being able to lock a cities population growth. Half the cities eventually get to a point where there is only 1 more food per turn available. Once they grow, they starve back down and do it all again. The starvation notices become annoying, and it's hard to know when a city is legitimately starving because of a terrain change of some sort (pollution, global warming).