I have very little interest in watching freestyle and I usually only watch the Olympics if it is an OSU wrestler. However, folkstyle rule changes that I would embrace are:
Don't stop the wrestling action just because a wrestlers hand or foot goes off the mat surface and if a wrestler grabs the edge it should be a penalty point (see Esposito against some OU clown years ago). It's a ridiculous rule as it doesn't prevent injury if they are already down on the mat. I mostly only watched OSU wrestlers during the NCAA but I lost track of the number of times this cost us points.
We are great at reversals. My wife, who has an average interest in wrestling, continually asks why a reversal is not worth 3 pts (1-escape, 2-take down). Every time she asks I say because that's the way it is. Dumb answer.
I know we are historically great at riding but maybe it would be a good thing, action wise, if after a minute riding time top man was given a point and put them on their feet unless the top man was trying to turn (ala freestyle). Of course this thought has been discussed for years.
IMO, Push-out points are dumb and just encourage the Iowa idea that just because a wrestler is pushing he is wrestling (also one of the reasons I don't really like freestyle). This style sucks! If the wrestler is trying to stand his ground (not backing up) and is pushed out, the pusher should be warned for stalling (pushing is not wrestling). I think that if all a "wrestler" does is push and never attempts a takedown, he is stalling.
The time the top wrestler has to return his opponent to the mat should be strictly enforced and the ref should immediately start a verbal count (like grabbing the leg) when the bottom man gets to his feet. And it shouldn't be time until an attempted return, it should be the time on their feet.
Even though we are good a getting near-falls, I am still not a fan of near-fall scoring as it now is. The most important thing in wrestling is the pin; going for a pin should be encouraged and rewarded. 2-count - 2 points; 4-count (or 3) - 3 points and only award the 4 points if the bottom man is in jeopardy of being pined. I love cheap tilts but I only remember one time seeing a wrestler pinned from a cheap tilt; that was by Jordan Oliver and you could see that his opponent was almost pinned before he was.