Re-Rolling All Hit Dice Every Level

From a 1st Edition AD&D Dragonsfoot thread: http://www.dragonsfoot.org/forums/viewtopic.php?f=1&t=69952&p=1625288#p1625288

It was noted by some members that the wording in 0e's "Men & Magic" concerning the accumulated hits of PCs might require players to re-roll their hit dice every time they gain a level. Apparently, this is a standing rule in Empire of the Petal Throne, but I have never read those rules, so I can only take it on faith that a lot of someone's aren't pulling my chain.

There are two ways to look at this interpretation of the rule, if used this way:
1 - The re-rolled hits stand, and PCs may wind up with fewer hits at their current level than when they rolled their hits on previous levels.
2 - The group may decide that no PC can lose hits when re-rolling, either standing pat at their current hits (even after re-rolling) or the PC is entitled to gain at least 1 hit if the re-rolled total is less than the previous level's re-roll for hits.
 

I've experimented with this house ruling, and the players I had at the time (5 or 6 years ago) hated it. Well, all but one adventurous player hated it. The player who actually liked the idea suggested the second caveat above.
 

Now, I think about the bell curve and the general law of averages when rolling dice, and I don't have any scientific evidence to back me up, but I think it is more likely to roll higher numbers when rolling a handful of dice every level than it is to roll a single die and adding it to the accumulated total.

I am looking to adding this variant to my house rules, so any feedback on the subject, pro or con is welcome!

Levels Beyond Basic assumes 4 related rules when considering hit points:
1 - Characters use the Hit Dice based on class from Greyhawk and Holmes.
2 - Monsters use Hit Dice from Greyhawk and Holmes.
3 - Weapons cause damage according to type from Greyhawk
4 - Monsters cause damage according to type from Greyhawk and Holmes

If the hit point determination method above is offered as a variant rule in Levels Beyond Basic, how would it affect the game with the 4 related rules? Would it offer players a chance to get better hits over time, or would it add an unnecessary level of danger to PCs with low hits?