Cant retract rear caliper pistons on '95 A6 - why screw?

[John Larson]

You asked: 

"So can someone please explain to me the logic as to why these are made in a
way that you have to twist and push? Seems idiotic to me - every other car I
have had, you just press them in."

You  must not have owned very many cars.  The "universal" set sold nearly everywhere has about 8-10 different adapters for various cars, and there are a lot more cars on which the tool won't fit.  Some adapters fit several makes/models.  The reason the front calipers on your car disn't need the tool is in the handbrake design.  The fronts don't have a handbrake, so the adjuster mechanism isn't present.  

John