I can't believe people worry about someone cheating on a hit point roll (and some of those same people are okay with a static HP boost that is larger than any hit die max result). If you are okay with big HPs, do you really care if someone fudges their HP roll? More importantly, why aren't players rolling their HPs at the campaign table, in plain view of other players? Even more importantly, why would you play any game (or even socially interact) with the type of person who would cheat on an HP roll (or try to cheat at D&D at all)?
The only time I've even wondered about whether someone could possibly even be cheating in D&D is with 4e rules, where the players have pages and pages of different numbers and keywords, more than any one person could keep in their head. It was either double-check every power someone used or just take them at their word that now they get a +21 and glowing eyes for a round or whatever. But even then I didn't "worry" about cheating because, wow, how low can you sink in life? So someone cheats at D&D- good for them. It got them nothing, and the act would almost certainly stick out like a sore thumb over time. Everyone would mock the poor schmuck- cheating to out-nerd his friends. Heck we might even give the cheater's character some bonus XP, just out of pity.
I want to assume that the "cheating" worry is a false one meant to over-emphasize the position of those who want to do away with the beautiful randomness of D&D, but then there are people who think Volvos are beautiful cars so it never proves productive to make assumptions about the beliefs of passionate people.
HD rolls are awesome fun and one of the things that is fundamental to my personal sense of D&D-ness. It's part of leveling, which is a ridiculous concept to begin with but one that is inextricable from D&D (though some edition will try to do with it someday, I'm sure). Easy-to-add options include minimum results or even auto-max HP for the HD roll for first level (a fairly common practice in plenty of D&D and D&D-like games from every edition that has HD rolls) and re-rolling all HD rolls that result in a 1 (though I usually only consider that last result for fighters).