Civilization – the difference between a missionary and a great prophet

• You get some turns of anarchy, which means your science, commerce and culture stagnates and you get a big penalty for production,
• You lose the policies in the branch you abandoned (no refunds).

Actually I think in some cases it still might be not such a bad idea to do that. Especially if you didn't invest too much in that policy and you are not going for cultural victory anyway. Some early game policies matter much less in the late game. For example you can use a bit of Liberty for early expansion and then abandon it for Autocracy.

I think a strategy focusing on great people can be viable - especially great scientists and great engineers, they can really make you leapfrog forward by saving many turns.

Is it useful to focus production on great people? Yes, I think it is. I've been experimenting lately with creating cities that focus on one type of great people, in order to generate them quickly. I think only the first few cities, the "major" ones, are appropriate for this strategy.

What you need is to:

1. Build the city next to a river or lake, in order to be able to construct a garden.
2. When you choose which wonders to build, make sure they all generate the same great-people type.
3. Obviously, try to get as many relevant specialist buildings as possible. I think, however, that it might be better to let the city grow for a while before you transfer citizens to become specialists.

Wonders are important for this strategy, so try to focus on them (and maybe also use Egypt and/or the +% wonder production social policy). The patronage social policy that grants great people from city-states is also nice, though a bit hard to get.

Though I haven't played a full game like this, on one of my games I have made an attempt to focus my capital on great engineers, and the results were pretty good.