That's the problem, there's so much pressure on the player from the outside that they really have no choice but to get back on the field ASAP. If you don't then you're soft, you're letting your team down. And it gets worse because of how easy it is to pass the concussion test (or to cheat), the medical staff will clear you when you know that you shouldn't be. So what do you do? Do you quit? Do you refuse to go out there even though the experts in that area are telling you that everything is fine and you're good to go? Because that's how the media is going to portray it, they'll show you on the sideline shaking your head refusing to get back on the field while the medical staff is clearing you. Your career would be over at that point, you'd be the laughing stock of the NFL.
But at the same time, what do you do? Do you suspend everybody that suffers a concussion for 3-6 months? Everybody would be placed on IR immediately. The league would be "dead", there would be so many star players missing. And if you ban everybody after 2 concussions, forget about it. The players will do whatever it takes to hide it. The least the NFL could do is be upfront about this. Tell the players, everybody, the media, fans etc. what they're signing up for. CTE, suicides, brain damage, Alzheimer, all that stuff. If you still want to play football you know what you're signing up for. It's on you. It's not any worse than breaking your neck and to sit in a wheel chair your entire life, that stuff happened as well. Players have died on the field. So concussions aren't the worst thing that could happen to you, but the issue is that the NFL is trying to sweep it under the rug because they're scared that they're gonna lose fans, that kids are not going to be allowed to play football which obviously will hurt the NFL bigtime if all the great athletes are now heading to the NBA, MLB etc. Sooner or later they have to admit what's going on, what everybody is beginning to see. I don't know what they're waiting for.