Right. I think it would be perfectly workable. The current system where you have basically 4 conserved resources, AP, HS, Daily, Item uses, seems to me a bit unwieldy. Item uses are fairly minor and most players don't seem to get too worried about their AP use since they get more fairly regularly, but once you burn the majority of a party's dailies or drain several of the PCs down low on HS the day is over. I think the renewal criteria for these is a bit too stringent. Merging these categories simplifies player decision making a bit and also allows for more interesting trade offs. A player is still going to balance slugging it out with encounter powers vs burning some resources to end the encounter quicker (hoping that the trade of HP/HS vs daily uses is favorable in the current rules) but now they aren't regretting making that specific decision later on when they see what the next encounter looks like. Instead they get to make their decisions more appropriate because they are always made on the basis of relevant information.
Obviously the potency of dailies, the hit point number recovered using a hero point, etc have to be balanced by the designers to make each option roughly equal. I don't think that's impossible to do. There is still complexity in terms of requiring healing powers to access healing, etc either.
I never played either of the Star Wars systems so I can't really comment on whatever issues there were with how it worked there, but I can only assume that the various uses of the points weren't well enough balanced. Some options must have simply been better than others?
In terms of recovery what I'm looking for is superior narrative control of pacing so that games can proceed at different game world time rates and not run into problems. As it stands now my own practices on HS recovery are more tied to narrative events than strict time. A "chapter" usually involves beginning with resource recovery and the action taking place during the chapter draws on that pool. It allows a much more literary style of pacing where a sequence of encounters are not slavishly forced into an artificial "adventuring day". Player choices can still determine points where the party can recover, but it avoids "we sleep in the dungeon" moments. The players know that they are going to have to manage their resources through accomplishing some sort of recognizable goal. Using hero points and allowing some ongoing recovery just helps deal with problems like "oops, you had some bad luck and got beat up, too bad I guess you'll have to all run away and rest now. Sorry the boss monster got away while you healed up from those 4 lucky crits I got."
I think it also allows for a variable degree of gritiness. In fact the gritiness doesn't really have much mechanical impact anymore. A gritier game simply spreads things out more in game time, so that nasty sword wound you got takes 3 weeks to heal? No problem because the narrative pacing of the adventure is simply scaled with that in mind. More tension can exist too since you have hero points which you may be able to gain as you go along it can make more sense to press on while your low on resources. You'll just need to take bolder actions, that is up the stakes of your encounters with the enemy, to pick up some more.
Admittedly some players will tend to feel overly entitled and may try to ham things up for points, but the DM knows all, its not like you can fool him into believing you took a big risk when you didn't. Maybe a system like that leans pretty heavily on the DM to do a good job, but then again 4e is already leaning pretty heavily on DMs in several ways. Published adventures are going to point out where points should be awarded, so it probably wouldn't make pre-made adventures any harder to run.
In any case I'm always looking for ways to reduce system complexity and usually eliminating several different mechanics in favor of one does that.
It would be interesting to know what the debate on this point was in the 4e design process. They obviously must have had some sort of mechanism like this on the table at one point or another.