Blue
Ravenous Bugblatter Beast of Traal
I think you'd have to be careful with this. 5e is designed around the assumption that low level characters rely primarily on AC for survival, while high level characters rely on hp. Going this route, you might end up with 20th level characters who are effectively more fragile than they were at 5th level. For example, it would be much more likely for a 20th level character to be one shot by Power Word: Kill, since it's far less likely that they will have crossed the 100 hp threshold. Now, there's nothing wrong with that per se, if that's the style of play you're looking to evoke, but it is something to consider.
Personally, characters typically start at 3rd level in my games. (I did recently make an exception for a group that is new to 5e; they started at level 1, and after I nearly tpk'd them with animated brooms in their first encounter, I scaled back the difficulty a bit for them.) IME, experienced players tend to find the first two levels a bit boring due to a lack of options, and by 3rd level characters are robust enough that I don't have to hold back.
I was addressing the OP's question about high level characters having too many HPs at his table in a positive way. If you don't like the basic premise, I'd suggest taking it up with [MENTION=82779]MechaPilot[/MENTION].
It's not a pain point at my table, I don't need this rule personally. Just trying to add constructively to the thread.