I think you could still keep hit points (or wounds, if you'd rather), since tracking health in some manner is pretty much in every
RPG out there, which suggests that there may not be a better (or at least easier) method to do it.
Of course the biggest change would come to casters. I think the best solution would be to go to a "casting check" system. Personally I would not set DCs to particular spells, but instead let caster make a check to find out how much magical energy they can gather that turn, and then decide whether to use it immediately, or keep gathering next turn to be able to use bigger effects or more powerful spells. It would require a totally different system for casting and using spells, but that would not necessarily be a bad thing.
I think something like this would require far fewer spells, but each spell given multiple options for each "point" of magical energy spent on them. It's probably easiest to imagine with harmful spells, since the more points, the greater the damage and/or larger the effect.
Perhaps something like this (totally
making stuff up here with no thought behind it; I'm sure it's full of holes):
Spells still have levels, but the levels determine how much Power is needed to cast the spell. This may mean that there are more than 9 spell levels.
A spellcaster can automatically spend an amount of Power on their turn dependent on their level. For the moment, I'll say it's equal to their half their proficiency bonus. So a 1st level wizard has two Power and can cast a 1st-level spell using their action.
In order to gain Power, the caster needs to make a check of some sort. Maybe's its a spellcasting ability check, maybe it's Arcana or another appropriate skill, depending on class. On a success, they gain Power. Maybe it's equal to half their PB again, maybe it's a d4 or other die. Maybe the die you roll goes up as you increase in level. On a failure, you either gain no Power, lose Power, or have a failure of some sort.
You can then (same turn) decide if you're going to cast the spell or continue to hold it and try to accrue more power next turn.
Casting the spell may also
involve some sort of check.
Possible complication 1: if you lose concentration on your spell while accruing power or fail to cast it, this could cause dangerous or disastrous results. This is to discourage spellcasters from spending a minute or ten gathering energy and letting loose a ginormous fireball
to toast the entire adventure location.
Possible complication 2: You can only accrue Power for a few rounds before you have to cast the spell. The number of rounds is dependent on your level. A low-level wizard simply wouldn't be able to get enough energy to get a ginormous fireball.
Possible complication 3: Each round you accrue Power, you have to spend 1 hit point.
You could do something similar with martial abilities, gathering instead "advantage" or something that enables maneuvers and abilities that otherwise would have been per x-rest. This is kind of the default for fighting in inspirational media, from anime to pro-wrestling, so it shouldn't be that hard to implement.
This one I'm less sure of. It's great for high-power fantasy but less for more traditional fantasy. In that case, maneuvers and the like are useful. This could
be combined with a "Power accrue" thing to allow for fancier maneuvers, but it might be easier to give fighters a certain number of points (or dice) each turn and fighters can choose to spend these points of maneuvers or increasing damage, to-hit rolls, movement, AC, or even saving throws.
I don't know if this is very D&D, but it could potentially be interesting.