The biggest difference between the system you devised and this one is, you have multiple pools of points. Here there is a single pool and if you use more dailies then you will wind up not using as many at-wills and encounter powers during the day. I think this self limits the daily healing powers.
Not quite...
All but 2 PP are recovered after each encounter or after a "rest". So after 8 encounters a character would be -16 PP.
So the Cleric can just rest one extra time and lose 2 PPs. Only two dailies are needed to heal everyone to pretty much full: Consecrated Ground and Mass Cure Light Wounds. In return, no one needs to use healing surges to heal during downtime. This only happens if the party has a Cleric or someone with similar powers; a Warlord cannot do this. Are you OK with the reduced demand on healing surges, and the increased power of Clerics?
The stun lock problem is in the system anyway - it is part of the game. For instance if various characters all take a stunning power they can hit a creature every round. Long story short this is not a problem insofar as the game system already has it.
Yes, but they can use the stunning power only once per encounter or day (most of them per day). Even the really abusable ones require a very high level currently, like the Paladin's Stunning Smite + the Demigod's Divine Miracle. There are ways to nerf a monster's saves so stuff like Legion's Hold lasts a long time, but if the monster gets lucky and rolls a 20 or the player misses, then it's gone. It's also usable only in one or two fights. With a mana point system, these limits are largely removed, especially if you can recover uses of daily powers easily.
My question would be is it really all that bad to to "spam" a power? Players get a better power and they use it more. Quite honestly, under this system they will try and get more "utilitarian-attack" powers rather than the more up front best damage/area powers. This would give them more versatility. When they know they can always use their best attack power every round (limited) it frees up their selections for sub-par powers that comes in handy in "specific situations". This could create more variety in characters. I likey.
Yes, it would be bad. Take, for instance, Blade Cascade. This Ranger daily power deals damage in the mid-100 range per use (this is after the nerf). Not only will the melee Ranger rarely use any other power, your monsters will also die very quickly. Additionally, all melee characters will probably try to pick this attack up and use it every chance they get. Alternatively, consider Divine Regeneration used every battle. With Regen 28, characters are extremely difficult to kill. Are you OK with that?
The 1 use of a power per day or encounter means if WotC messes up and creates an overpowered power, then the effects are still limited. A lazy method of balancing powers IMO, but an important one given the powers currently in existence. Removing this barrier means you have to nerf the overpowered powers yourself.
If you want to use a mana point system, go for it. I think the flexibility of such a system would be more fun than the current 4E system. Just be aware that you have to do a lot more thought and work to prevent it from being broken.