I loved how you touched on how playing higher tiers builds consistency for the lower tier mechanics. your example in this case was a crouch det for demoman and in jump if your crouch det is bad it will hinder your ability to finish a higher tier jump but in 6s if its derpy it could end up ruining your whole uber.
I also appreciated that you brought up the "freestyling" aspect that having jump mechanics down allows you to make something up on the fly (sorta seeing the 6s map as a jump map itself). while i think its more applicable to soldier in finding a random way to ramp slide in and collect a medic pick or something like that, demoman i think equally has the ability to squeeze his way through a doorway at just the right angle with a sticky jump as to be unexpected and similarly collect a medic pick or what have you.
good video