That works great, if you just want to capture cities to sell them. And that's a good objective.
But I capture cities to keep them, grow them, and produce. I take them only if they have a strategic importance... either they have a lux res, or they are on the coast on the side of the continent that I need to have a port on, or they have extra food or gold or iron, etc.
So I pick my cities carefully before conquering them. And when I do conquer them, it's for keeps. For this objective, I find it best to annex right away and build the courthouse right away, clearing forests to speed-up the courthouse construction.
For culture, the hit I take is short lived when annexing. Besides, monuments and temples are among the first buildings I build in all my cities. I usually start with the granary first, then the monument second. After that it depends on whether I can build a water wheel or stone works. Then aqueduct, market and temple, the order of which depends on my research progress.
I then get extra culture and extra happiness through social policies, especially the policy that gives you 1 happiness for each monument and temple in your cities.
So from the loads of culture I gain from all of the above, loosing a little culture from an annexation is like loosing a teaspoon of water from a bucket. Besides, once I build a monument and temple in the annexed city, I'll be getting culture from it for the rest of the game.
But then that's just my way of playing. That's one really great thing about this game, you can follow any number of paths. Just like a real civilization, I guess.
But I like your strategy too. I'd like to try it in a really short game.