I know this may not be the most popular opinion on this site, but I'm going to call it like I see it, and I definitely see a pretty negative side effect of the rule that not a lot of people are talking about.
One of the things non-soccer fans here in the USA love to rag on soccer about is the amount of fake injuries that sometimes take place. Now I know a lot of non-soccer fans like to explain this away as "all soccer players are a bunch of [female body part]", as they laugh until their beer guts jiggle and they have to catch their breath. Now I'll be the first to say, I hate this trend in the sport as well, but there is a clear cause and effect. When a player acts injured after a foul, the ref is more likely to give a card to the opposing player. It sucks, but it's human nature. The athlete's reaction to the foul (or hit) plays a big part in how bad it "looks" to the official, who then has to make a quick decision on how to assess discipline.
Now I know we all like to think of our football players as tough guys that would never "act" like those wussy soccer players, but ask yourself this, if Shazier lights up a kid on Northwestern in the 2nd quarter of a close game, and it's questionable, do you think that Northwestern kid will stay down a little extra long? We see embellishment in hockey quite often, and those guys are pretty dang tough.
I just think we're going to see a lot more laying on the ground, hands to the face, acting, after big hits in college football this year.