This will sound silly - I hope it doesn't - but I was suddenly struck by this idea: in all martial arts, you will fall down and have to get back up. To borrow the name of, ahem, Another Martial Arts Web Site, how can we separate the "bullshido" from facts - facts based on how the human body works in gravity - about how to fall safely and get up again safely? When I first began to train I spent a year or more just practicing forward rolls on my right & left sides. Backwards rolls took a couple years more. I don't think I can practice rolling enough. The same with what I call "standing" side-falls.
I thought most "throwing based" MAs practiced breakfalling in a fairly similar manner. It seems reasonably well-established. It would be "bullshido" if they taught something which it could be proven didn't work, but since there are plenty of people who can fall without hurting themselves and get back up again, I don't think it's all that contentious.
Really stupid things. Of all the grappling martial arts I have encountered wrestling is the worst offender. No ukemi, putting out their arms (and wrists) to break their fall... it hurts to watch. It's just not taught which is sad. It's pretty simple to tell whether your break falling is effective. If you are falling and hurting yourself then they are not effective, if you do not hurt yourself, then it is effective. Pretty simple.
Ukemi. It's intuitive, but with the throws they use and the intensity they do them at, they have good breakfalls. Especially greco guys. It just doesn't look judo.
I've never seen a wrestler use ukemi, generally the only thing I see them do is hold on to the other guy.
There's a lot of information already around here on ukemi and breakfalling. Depends on the throw how you fall and how you control yourself in the air.