AI and chopping forests

Is it just me, or does the AI seem to put off chopping forests for a really long time? In several of my last games, I've noticed AI capitals surrounded by dense forests well into the classical age, many times far into the medieval age as well. In my most recent game, I was able to conquer Huayna Capac's capital around 1AD (with a handful of horse archers, nonetheless), and it was still surrounded by forests, with hardly any improved tiles.

I think this is a huge handicap to the computer. Chopping forests gives fast hammers for crucial buildings/units and frees up space to build other improvements (which may be part of the reason why the AI techs so poorly, tons of forests, no cottages).

By the way, I play on prince, so maybe this is less of a concern on higher levels when the AI starts with a free worker.

I lack of cottages is generally thier problem, but you don't need to chop your forests to do that.

Another problem with having forests around a city is that they provide a handy place for a attacking stack to camp out in before they assault the city.