I'm fine with the fixed HP approach 4e uses. It seems most that like the random rolls don't have the courage to go all the way anyway. People create a random + fixed hybrid system (i.e. D8 = 4 + D4) that more than not simply awards more HP than the players would have had anyway. In older editions I've played, we always allowed rerolls on 1's and sometimes 2's as well. Which kind of again, defeats the purpose of true randomization and usually ends you up above your expected average, which of course all players like.
My impression from the old systems, was that Constitution was the thing that was supposed to save fighters, or other classes worried about HP, who rolled low. A 1 or 2 is bad sure, but when you are still getting 5 or 6 anyway because of your 18 constitution it doesn't hurt as much.
That was one real boon of the old system, not the dice roll itself, but that you could have a modicum amount of control of your HP vs your expected average simply by how much you wanted to spend or could luckily afford on your Constitution and in turn, bonus per level. I miss that far more than rolling D4 as a Wizard for example.
Then again, my groups discovered long ago that at 1st level CON = HP went a long way to extending the life of characters vs the ridiculous chance of rolling 1 or 2 HP at 1st level. So after that point, you could afford some poor rolls at higher levels, because you had about a 6-10 point cushion to fall back on. It would take many bad rolls to make you fall behind your normal expected average and of course more than not, most characters would end up doing better.
For a concerned DM, random was never really 'random' anyway. A Fighter who rolled low HP for a few levels just happened to get some magic armor +1 better than was initially planned, or the party happened into more healing potions or scrolls than they might otherwise. For the 'unconcerned' DM, that Fighter simply met a early end, sometimes intentionally and suicidally, and the player came back with a new one who had the stats he would have preferred the first time around. Mostly a huge hasstle and timewaste.