I'd expect that it's part of the picture for some guys, but it's not a categorical explanation.
There are football players of all kinds of personality types and a fair number of physical builds, but it disproportionately attracts guys who are big, strong, athletic, and enjoy violent collisions. A lot of those guys would still have a violent streak if football had never been invented.
Then you add PEDs, a very macho, aggressive culture, the uncertainty of short careers and little guaranteed money (for most), plus a lot of wealth and social attention, both good and bad, before you get to the head trauma. Some guys are fine with all of it but it's a pretty toxic cocktail for a decent percentage.