NOTHING stops the brain from bouncing off the skull after impact and sudden stops. Extra padding helps with the comfort OUTSIDE of the skull. I have also always said that the "safer" helmets have become the more we see players leading with their heads. Back in the day, minimal head contact would snap your beak in two. I also wonder if tight jerseys without sleeves has hindered things. Less to grab = more hits.
CRAP "tackling" has to be the #1 problem. SOOOOO many players throw themselves head DOWN and first, instead of WRAPPING! It's why we constantly see the cliche "highlight" of ball carriers hurdling Defenders.