Your argument is largely nonsense, although the gist of it isn't and actually has some sense behind it, not unlike the talk of removing gloves from boxing, where bare fists do more damage but tend to make things quicker (i.e. KTFO faster, cuts that deem ending the fight), and there's some sound thinking there. The thing is, you're not wearing helmets just to protect against helmet to helmet, you're trying to protect the head in general in a sport with lots of contact, so its tough to argue players would be safer without them. Address the head hunting directly, as you'll still have to address it if they had helmets or not.
Plus, you don't want a return of old school hockey look for your players.
Now, maybe you could argue for change to different helmets which I think could make sense. I mean even bull riders wear hockey style helmets these days.
Lastly, I don't think rugby tends to have such variety in players. I don't see a lot of 350lb rugby players (and doubly so don't recall seeing teams with 5'8 185lb players going up against 6'5 300+lb players), although that might just be my own ignorance of modern rugby and it actually does happen. There's a good amount of other rules/general play aspects that make an inherent difference between the two sports that I don't think its a good comparison. Also, I'd guess that most rugby players should be wearing helmets. Hell, soccer players probably should too. Certainly there's some risk that the players on those sports might feel like that grants some extra safety and so increase the amount of risky behavior they attempt, which you'd need to address.
Oh, and I think it'd be a hard sell to the players (for appearance purposes, although plenty would like to show off their face/hair more I'm sure), and teams (branding).
Lastly, I don't think rugby tends to have such variety in players. I don't see a lot of 350lb rugby players (and doubly so don't recall seeing teams with 5'8 185lb players going up against 6'5 300+lb players), although that might just be my own ignorance of modern rugby and it actually does happen.
Even without helmet-to-helmet contact I think you'd quickly see a death or at the very least a serious permanent injury in football without helmets. The game is played very differently today and at extremely high speeds.
Can you imagine being a170 lb DB and lowering your head to try and tackle a full speed Gronkowski or Derrick Henry in the open field without a helmet?