I do care about balance issues and I think that you illustrated the balance right there in your quote. "You want people to use their daily/encounter powers more, but you punish them a lot (as in make them useless) if they use their powers too much." If a character is going to use their powers frivolously and without abandon then they should be caught with a crossbow only barely being able to attack. How quickly we forget how a wizard worked before 4e.
I suppose the heart of this HR makes dailies expensive encounter powers and makes at-wills inexpensive encounter powers with characters becoming less powerful after each short rest.
First, let's take a look at the number of powers used issue. Let's suppose we have a level 30 character with a 30 in his primary stat (Demigod required). Normally, this character would have 4 dailies, 4 encounters, and 7 utility powers, most of which are dailies. We can assume he'd use all 4 encounter powers and 2 daily powers (one of them a utility power) per encounter, along with 4 at-will powers (9 round fight). In your power point terms, this is 2x10 + 4x5 + 4x1 = 44 power points.
Thankfully, that level 30 character would have 45 power points so he's fine, right? Well, after he rests he loses 2 power points and can no longer fund this power point usage. So after a couple of fights he can't use as many encounter powers, or subs an encounter power for a daily power. This should make a fight harder. On the other hand, he gets to use his best powers over and over again. That should make a fight easier. What is the net effect? Would fights get harder or easier?
This is what I mean by looking at game balance, and unfortunately I don't see much analysis on this issue. This is also why I don't think this system will accomplish your goal of allowing people to use their powers more.
Actually, I think this would make the fights even swingier and more dependent on luck. The fights would only be easier if the players get the benefits of using their better powers multiple times, as in they manage to hit. If they miss, the effects of having fewer powers will make the fight harder. In the extreme case, if the party is out of power points, the fight is over since at least half the party can't even hit with an attack anymore (the half that don't have good Str/Dex scores). Even if it's not so dire and only a couple of players run out, those characters might as well have died when they run out of PPs. They can't do anything, and that's what gets players to stop paying attention and start surfing the web/reading magazines.
That could easily happen; suppose it's their 4th fight of the day, which means -6 power points that translates into one less encounter power and one less at-will power. That leaves them with 2x dailies, 3x encounter powers, and 3x at-will powers, enough for 7 rounds of combat. I'm pretty sure it's not a rarity for combat to last longer than 7 rounds, especially if there's a bit of bad luck on the players' part. Sure, they could trade out an encounter power for 5x at-will powers, but then the party would be much weaker.
Second, the reason I assumed you don't care about balance issues as much is because you brush off a lot of other balance problems a power point system can cause. A party with a Cleric is a lot stronger than a party without a Cleric because the Cleric grants the party free "healing surges". The game assumes healing surges are a scarce resource, and this breaks that rule. What are the consequences? How would you fix that? I don't see anything on this.
In normal play, if a power is too strong, its effects are limited in gameplay because it can only be used once per encounter at most, and usually only once per day. Regeneration 30 is pretty crazy, as is doing 150 damage with a standard action. With a power point system, you have to nerf these powers or otherwise restrict them, or other powers will pretty much never be used and fights get much easier (or luck-based). How would you fix this? I don't see any analysis on this issue.
Hence why I asked you what your vision of a power point system is. It's clear we have different views on this issue, and in order for us to help you decide whether your power point system suits your goals and what improvements you can make, we need to know what your goals are.