I was also a fan of random events in BTS at first, but they quickly became annoying. Case in point, from a game I am currently playing. I was building the Colossus in one of my cities. One turn before I was about to complete (one turn!), the city got hit by a hurricane (or something). I was given the option to select buildings being destroyed or citizens being killed. I would like to select the citizens option, but it is grayed out (I've never actually been able to select that option--it always forces me to select buildings). I have no choice but to select buildings, and as chance would have it my forge gets destroyed. I lose all production on the Colossus, don't get any money for it, and a few turns later a rival civilization builds it.
I really liked the quests in BTS, but the random natural disasters or weddings screwing you over all the time? Not really a big fan of those. So I will join Giant Dwarf in saying good riddance to BTS-style random events.
(Yes, I know you can turn off the random events in BTS, I just keep forgetting.)