4E milestone mechanic is interesting as a basic concept. Instead of having a fixed "Daily" thing, you basically have to achieve something in game (Beat encounters is 4E take, but it doesn't have to be that) and recover some ability (in 4E, it's not actually recovering an ability but gaining a different one in form of action points).
I think that works just great for non-magical abilities in D&D. Depending on what you do, maybe you can use your Brute Strike once per day or 20 times a day.
It can be more complicated in other areas
1) Vancian Magic. Having a non-predictable moment for an abstract martial maneuver to recover works, but if the idea of Vancian magic is that you consciously prepare a spell, then cast it, and then prepare a spell again, it seems weird when you recover spell slots seemingly random. But it only seems weird because the "Daily" nature of Vancian magic in D&D is so ingrained in us. In the end, magic can follow any arbitrary rule and doesn't have to make sense to us, since it's magic.
2) Healing physical damage (be it hit point damage or a real wound system) via such milestones doesn't work so well to be believable.
So, my take would be:
1) hit points are explicitly never physical damage. But taking hit point damage can cause wounds. (specifics to be decided, but for example, everytime you lose 1/4 of your total hit point value, you suffer a wound, or some such)
2) You recover hit points via a limited set of recoveries.
3) You may be able to ignore most wounds most of the time, but they can lead to penalties and death.
4) Any wounds you suffer require rest to heal, and that rest can be significant. Magical Healing of course could fix them in any manner.
5) Characters have access to certain special abilities. Each has one or more uses. Some abilities may be flexible in what specific effect they have (basically, something like psionic power points where you can select which power you use)
6) At certain intervals or to certain occasions (for example, you kill a foe, you complete a combat, you kiss a princess, solve a murder, achieve a long-term character goal, reach an important location, spend a standard action studying an object), you can recover some uses of abilities. There can be special rules for this - maybe a Wizard regains a spell slot but must still spend a few minutes to prepare a spell in it, or maybe you recover abilities based on groupings by power level or thematic relevance. (Say, you can only recover 1 Lesser Akashic Memory and 1 Greater Akashic Memory, instead of any 2 of your abilities, or you recover only social abilities after kissing the princess.)
Time is only used to recover stuff that is highly "physical", like wounds or your weekly rent, but not for more "gamey" resources - like tactical maneuvers, spell, action points and so on.