I was looking at the minor calamaties and was noticing the lack of mitagating civ advances for them.

Was this intentional to speed up their resolution? If an advance was selected to just negate the calamnity that wouldn't slow things down (and would actually be slightly faster.)

I would guess it is this way, so you don't have to take into account advances' mitigating effects when deciding the cost of the advance.

Now, why would one want that? Because the minor calamities aren't in play if there's less than 7 players.

Yep, Pureblade got it. I might not have had that specified yet when BB posted his question though.