You don't have to bowl short to hurt someone though, on a quick track a tall bowler is perfectly capable of getting someone in the gloves or body just bowling length balls, or break your toe with a yorker. Bowling short is (mostly) a tactic to get people out, whether caught or pushing a batsman back before getting them with a full a ball. In any case, a beginner amateur player is very unlikely to be playing on a quick enough track with fast enough bowlers to get hit in the head too often! People bowling fast at you with a very hard ball is a pretty central part of cricket, I don't think I've ever seen anyone seriously into the game put off by it (the only articles/comments I've seen seriously suggesting banning the bouncer after Hughes have come from non-cricketers). It's a test of courage as much as anything else, leaving and dodging bouncers well still requires the courage to watch the ball closely and keep calm. If you do those things, bouncers don't pose a threat and you won't see the bowler sending too many more of them down! This will come with experience I should add, I remember being as scared of the ball as anyone else as a young kid, but the more you see of it the less it bothers you. Batting is more than a physical skill, it's about finding the balance - between attack and defence, between forward and back, between playing and leaving. If you make the bowling predictable and full only, that is killed off completely and it would quickly become more like baseball. I certainly wouldn't enjoy the game, the physical threat and short reaction times is a much of a key component of the battle against fast bowling as turn is to spin - removing the seam from the ball so it wouldn't move off the pitch would be as much of a disaster as banning the bouncer.
Also, how on earth would you enforce a ban on bouncers? Bowlers get things wrong, sometimes they bowl a wide, sometimes they dig one in when they don't mean to. I'm a pretty tall guy, on a quick pitch the difference between my normal length and a ball that would be shoulder/head height to a shorter batsman isn't much more than a yard or two. There's many guys out there taller and quicker than me too, what do you do when they miss their length and bowl one at the body - ban them from bowling? That would lose you players as quick as anything I could think of, you'd kill fast bowling completely.