Late to the party here, but I've been mulling this over since starting to follow freestyle wrestling a couple years ago. Freestyle is quite fun to watch - more action, shorter matches, more accessible ways to score, more motivation to be an offensive vs a defensive wrestler. However it isn't perfect - there's not enough riding. But maybe folkstyle has too much riding. I think you could have a really cool hybrid style. Let guys wrestle in shorts and without headgear, similar to freestyle. Maybe 2 stall calls on the bottom guy gives the top guy a point and puts them back on their feet; likewise, 2 stall calls on the top guy gives the bottom guy a point and puts them back on their feet. Give one point for greater than 45 degree exposure.
What's clear to me is that stalling calls need to be more consistent. I like how freestyle has several refs - this could be a fix here. As far as a push-out point, folkstyle nearly has that with the new stall calls on the edge of the mat but again, this is wildly inconsistent and the criteria for the call is weird - push a guy out and it's stalling against the offensive guy? But "stop wrestling" at the edge of the mat and it's stalling against the passive guy? Pretend to take a shot or circle and it's not stalling? It's murky as heck. I think if you just made it a clear-cut "step out and your opponent gets a point or a stall call", it clears up all the murkiness around the edge-of-mat stall calls. Yes, you may get a little more Iowa-style pushing, but I don't think I care about this... it's another way to score points and when I watch freestyle, I don't see guys only pushing the whole time because that approach opens the pusher up to all kinds of counter-based takedowns by the guy getting pushed. Freestyle has it's own murkiness for sure with the shot clock, not a huge fan of this but again as a newish viewer maybe I haven't gotten the hang of it yet.
Folkstyle is about talent and endurance. Freestyle is more about just talent. Are you better than your opponent? Prove it right here, right now. Folkstyle requires you also to outlast your opponent... which has it's own benefits and philosophy and whatnot but as a 30 year fan of folkstyle wrestling, I'll gladly admit that I get bored in a lot of folkstyle matches. No wonder it's hard to get new fans interested when many matches consist of primarily collar ties, weak attempts at pinning, and far too few stalling or stalemate calls. There's frankly not a lot of procedural motivation for guys not to save their gas tank for the end of the match or the end of the period. And I get it from a conditioning standpoint - no way could I go out there and go hard for a full match. But maybe the periods are too long. I do like the three period setup of folkstyle... maybe the periods could each be reduced by 1 minute or something combined with more mechanisms to break up slow riding action as I mentioned above.
Also, folkstyle overtime is weird. I'd be thrilled if they did a couple of sudden victory minute periods and then got rid of the ride-outs. Replace the ride-outs with criteria victory based on shots taken, stall calls, things like that. Lots of combat-based sports use criteria to award victories.