DM: ... so now that you have a new level, Bore'me, go ahead and roll 2D6 for your new hit point total.
Bore'me: [rolls] Ah, sweet! A 6 and a 4! That is much better than the 1 HP I had at first level!
Gimlet: Wait, hold on. What's that?
DM: What is what?
Gimlet: Bore'me rolling his first level hit points over in addition to rolling his second level hit points.
DM: We're playing OD&D Rules and that is one of the rules. You re-roll all hit dice upon attaining a new level.
Gimlet: That's a stupid rule.
Groin: Stupid or not, it is an OD&D rule and we're playing an OD&D game.
Gimlet: Not only is it stupid, it is an unfair and unrealistic method and I request it be reconsidered. Blah blah blah...
Gimlet: Blah blah blah... as you can tell, I'm incredibly passionate about this topic.
Eggoless: I too think it is ridiculous, but the rules are what they are, however much you, or I disagree with it. When I am a DM, I never followed that rule for the very reasons you've stated. It just doesn't make sense.
DM: Ok, let's end this discussion and move on. At least 50% of the reason for running this campaign under OD&D rules is experimentation. If Gimlet and Eggoless want to, I'm perfectly willing to use the two of them as the control case for not re-rolling hit points. If you both say yes, then from this point forward, your characters will both use the more commonly accepted method for rolling hit points where you only roll one hit die when you level and add it to your previous total.
If you roll an 8, then you get 8 more hit points at second level. If you roll a 1, then you get 1 more hit point at second level. The rest of the party will maintain the original OD&D hit point rule and we can see how it plays out.
Eggoless: I personally don't care, either way, but I will continue to go with the originally stated rules and re-roll all Hit Dice at leveling. (This decision isn't at all because my current hit point total sucks.)
Gimlet: Yeah, I'll stay with the rules as they exist.
DM: Er... so after all that, you just want to use the same rules as everyone else? Ok, then... I guess that issue is resolved. Let's get back to the campaign.
Gimlet: So just to make sure I understand this... when I reach level 10, I'll roll 10D8 for hit points?
DM: No. You'll never reach level 10.
Gimlet: Why not?
Groin: Because you're a dwarf and dwarves never progress above level 6. It's in the rules.
Gimlet: What?? Not only is that a stupid rule, it is unfair and unrealistic and I request it be reconsidered. Blah blah blah...
DM and most of the rest of the party: ...