Yeah. But if you said out until the next change of possession you could make the penalty so steep for going in early that no one would try. Go in early, ejection. Opposing coaches would watch for it and help the refs out if they didn’t see it.
I don’t think penalty is any easier. Often times the ref doesn’t see them go down, so you’re basically ask them in a lot of cases to blindly decide if injury is real or fake. Also, if I have a guy who is injured but could run off the field…I want him going down…and I think that’s okay and good. But if they can run off the field it looks like they are faking. I get poked in the eye and I need to come out for a few plays. I’m running off the field and I go down so we can get a sub without getting caught between plays…now I get a 15 yard penalty because I just went from jogging to down on the ground? A fairer and easier “penalty” would be to not try to make a judgement call and just make it clear cut. You stop play, you’re out until a change of possession. Easiest for officials IMO