Adults don't ride BMX bikes? Crap, nobody told me!
39 yrs old, 6ft tall.
Personally, I love the way my bike rides & fits. Sunday Funday! w/ 21"TT. 180 cranks, 8"tall bars, cut to 26" wide.
As far as your feet hitting, well that's gonna happen. Occasionally my heel clips the rear peg (Size 10 shoe, short chainstays) but you learn to place your feet on the pedals to avoid that. I've never had my feet buzz the front tire on a 20" bike, again you likely just need to learn to sync your pedaling with your turning. For example: turning left? then your right foot should be towards the back of the bike. Just like when you lean into a turn, you raise that pedal to avoid pedal strike.
So look for a bike w/ a longer TT and just spend some time riding. You'll figure it out.
Also, most cheaper bikes are simply shorter. (20"-20.75"tt) to get a 21"tt on a complete, you usually are looking at $500+ bikes.