I'm not sure if they are completely random or whether the selection is at least partly based on your play style. Did you play three very different games?Ive had the same crisis in all 3 games in both ancient and explo eras.(plague and religious) If i keep getting the same ones, i might as well turn them off.
With that said, i dont think they are that strong. If you are in a weak spot, they will hit a lot harder.
I had all the antiquity crisis, and I always got the "worst": plague in a militaristic game with many units, barbarians in a peaceful game, unhappiness in a game where I had way too many settlements.