I agree this (soft vs short vs crosswind including direction of
crosswind takeoffs, and landings) and how to prioritize combinations,
or anticipate problems was not well covered in my ASEL training - or at
least I didn't pick it up.

I could just as well have rolled my (then) new 172M in a ball in a
higher altitude crosswind takeoff. Luckily the strong crosswind
happened to be from the right. It wasn't until a year later that
someone else pointed out that the crosswind and its direction, has to
take control input and performance precedence.