The disadvantage of the old leather helmets (or the head guards they wear in rugby) is there is a greater risk of bumps and bruises, broken noses, etc. The advantage is that those injuries are relatively minor and they condition players to be much more careful with their heads. Rugby players are trained to put their head to the side of the player and push through with their shoulder, driving them into the ground in a way that spares the head direct trauma.
The advantage of the plastic helmets is that they do an excellent job of protecting the players from these minor injuries and in many ways make playing a more pleasant experience. The disadvantage is they do
such a good job of protecting the players from injury that the injuries that do occur tend to be of the catastrophic type: concussions, skull fractures, even spinal fractures. They lull players into a false sense of security, to the point that they seem to think they are invulnerable to direct blows to the head. This results in cocky, aggressive young men using their armored heads as weapons to intimidate their opponents. Most of the time they can get by with it, but when the unthinkable happens, it can be career ending or even lethal.
I would not be opposed to a return to the soft shell in football, but people would have to recalibrate their expectations of the product on the field. It would not be quite the same high-flying, violent circus act it is now. It would be a slower, more methodical game, much like we see in the old highlight videos. I personally don't think that would be a bad thing. Perhaps we'd see more of a return to strategy instead of the unending track meet.