The good thing is that a DM can match the party against, probably, twice as many monsters of CR1 or less straight away and have dramatic battles right away (cause i don't think 4 PCs fighting 3-4 Orcs is very impressive).
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Some how a slower HP proggrassion strikes me as leading to more tense combats and a more agreeable game style (for me atleast).
Seems like you want to flatten the curve - more power at low levels and less at high levels. If 4 PC's fighting 3-4 Orcs isn't impressive enough, how will it feel at 15th level if the characters are less than capable against typical L15 opponents?
Udalrich's example showing a difference of 96 vs 115 hp for a 16 CON fighter at 13th level seems to indicate this makes a pretty limited difference. Bump that CON to 18 (or take the Toughness feat) and he's back up to 109 hp. If we make him L20, he would have 175 hp (old model) or 130 under your model, so a 45 point drop at the high end and a 13 point bump at L1.
A 12 CON wizard would have 18 hp at L1 instead of 7, and 56 at L 20 instead of 74, an 11 point swing (only a bit less than the warrior) at L1, and an 18 point swing (much less than the fighter) at L20.
Is that enough of a change to meet your goals?
At lower levels, it seems like it would be much easier to just start PC's at L2 with max hp. Now starting characters can take more punishment, but the world need not change to accommodate them. You discuss raising enemy CR's at higher levels - do they need to drop at low levels now that PC's are so much heartier?