I think that's where the idea of 4E/2=5E comes from. Because that's almost literally the math. In 4E it's +1/2 level; in 5E it's 1 + 1/4 level. In combat, most 5E character are doing about 1/2 the damage they were in 4E, but monster hp (or rather encounter hp) is about 1/4 what it was in 4E.
Though it's worth noting, due to +Con per level
on top of your class HD, 5e characters end up overtaking 4e characters in terms of HP. E.g., take a Bard at 1st level with 14 Con in both editions: the 4e version has 12+Con score = 26 HP, while the 5e version has 8+2 = 10 HP. Huge difference! But then if you scale up to level 20, the 4e Bard gets only 5 HP per level, while the 5e Bard gets 6.5 average (or 7, if using the static HP rules). By level 11 (9 if using static HP), the 5e bard catches up to the 4e one--and exceeds it from there on. If you give both Bards Con 20 instead, they'd start with 32 (4e) vs 13 (5e), but now the 5e Bard gains a whopping 9.5 average (or 10 if static) while the 4e Bard still only gains 5. After merely hitting level
6 (5 if using static HP), the 20 Con 5e Bard overtakes the 20 Con 4e Bard.
(I am of course ignoring the effect of the meagre +1 HP you get at level 11 as a Bard--it makes no practical difference in context.)
The difference becomes more extreme if you look at lower-HD classes, and likewise becomes less extreme for something like Barbarian. But it remains nonetheless: 4e characters start beefier, but are inevitably overtaken by their 5e counterparts. For sufficient Con mod, 5e characters can have 50% more HP than an equal-level 4e character, meaning even if you treat one 4e level as "two-thirds" of a 5e level, the difference remains.
I wonder what would be the gameplay effect of requiring the expenditure of Hit Dice to get the full effect of healing word and cure wounds. For example, healing word allows you to spend one Hit Die to regain 1d4 hit points per level of the spell slot expended. If you are out of Hit Dice, you only regain hit points equal to the spellcaster's ability score modifier. Similarly, cure wounds allows you to spend one Hit Die per level of the spell slot expended. If you are out of Hit Dice, you regain 1d4 hit points per level of the spell slot expended.
In this way, it is more resource-efficient if you spend Hit DIce during a short rest (even if you don't have a Constitution bonus, you won't need to use a spell slot). It might even encourage the PCs to take more short rests!
It's possible that it could be done. But I am leery of doing such a thing without significant testing. Changing the core function of a major subsystem, such as healing, has lots of knock-on effects for a game's experience. It's not easy to predict how that will affect things, particularly since 5e has gone back to the "pay no attention to the
man mechanic behind the curtain" style.
Seriously, who the heck fights a SINGLE monster?! That sounds terribly boring and a waste of time. Just two to three dudes standing in front of a lone Ogre going "I attack!" until its dead? THRILLING stuff!
I mean, D&D has a handful of monster ideas (older dragons, beholders, mindflayers, liches) that make sense as solos. I would also say that 4e had plenty of good ideas for how to make a solo interesting. One example I've seen was a DM that made a solo encounter that changed form three times: once at bloodied, then becoming a
different creature when dropped to 0, then changing again when that creature got bloodied. Great fight, though I admit part of it was that the creature--a guy named Gregor--was very hammy and memorable on his own.
