Usually i left them enabled in my HoF games.
I've seen everything:
- pastures destroyed (and in the early game this can be a serious problem)
- pastures built (and this helps)
- Ice sculputure in tundra city, usually, and if you got enough money the free GA is a good boost
- some nice quest: the libraries one, that gives one more S to your GLB, and this never disappear, the colosseums one, together with SoZ starts a GA, the harbors one, the best reward is the free Nav1 for all your present and future ships, even the holy mountain (i don't remember exactly, but the reward was good)
- the inflaction reduced if you're running free economy (a good boost for SC and time VC)
- the comet fragment, nice for a SC
- 3 AIs destroyed by various barb uprisings in the early game in a non-HoF game (i owned the GW)
and a lot of minor events, usually balancing themselves.
The gold/iron/etc popping from a mine is there since Vanilla.
So, i keep them: usually their benefits are worth the bad ones, and there's some more fun.
Often i got a CR2 Mace defeated by a Sword in a city bombarded to 0: this is civ, remember?

i clearly do, playing civ since the Civ II era.