I tried to find the details about the current mini-forks but I couldn't. Do you have a link? I guess the number is small because the mining pools are well connected and none of them want to waste resources (because they loose money).

Probably 3 forks is a good number, but I'd like to see some data. Anyway, it's a linear problem that is adjusted automatically by the difficulty to find the next block. It's not an exponential problem that makes the protocol unpractical at scale.