In 3e, the game was shifting to encounter based systems. Book of nine swords is the best example of this. In 4e they threw that out and split powers into at-will/encounter/daily/ritual powers. I don't like at-will or daily but really like encounter powers and rituals.
At-will powers suffer from being too at-will. The image of the wizard eventually knocking down a wall by magic missiling it endlessly escapes my believability standards. At least martial characters can dull their axe or run out of ammo with their at-will powers. Also, what exactly is the purpose of basic attacks when there are at-wills?
First of all, the answer to your question about "what exactly is the purpose of basic attacks when there are at-wills" is twofold:
(1) Sometimes you are granted a "basic attack" in particular situations, like OAs or Commander's Strike.
(2) Sometimes you may be in a situation where you can't use any of your at-wills, like if you're a fighter using a bow.
Aside from that, I'm not really sure what the problem is. Here's what I see is the main problem you've mentioned:
I don't want players to be able to repeatedly use their attacks outside of combat to say, bring down a castle wall by hitting it with a sword several hundred times.
In that case, I'm not sure how your proposed removal of at-wills will help. Someone could still do the above with a basic attack just as easily as they could with an at-will. And you obviously want each character to have at least one power (even if it's a basic attack) that they don't run out of, otherwise they would "run out of powers" and have nothing to do. The reason wizards now have at-will magic is to stop precisely this problem from earlier editions where they would use up all their spells and then have nothing useful to do.
In any case, if you wanted to limit out-of-combat power use, since there are few rules for out-of-combat power use that would have to be done with a houserule either way.
Daily powers are just a limiting factor that I thought was trying to be abolished in the 3e ruleset, yet here it is in 4e. I have seen various threads trying to basically get daily powers to be used more for various reasons (hated when they miss, want monster to die more quickly, power point system etc). So, there is some like for systems like this.
I assume that by "limiting factor" you are referring to the fact that it is a resource that only renews at the end of each day, so players have to conserve it. So as I understand it, you essentially want each encounter to stand on its own with no resources carrying over from encounter to encounter. Is this correct? (If so, does it also apply to healing surges, APs, and Magic Item Daily Powers, which also don't refresh until the end of the day?
If this is correct, a very easy thing to do is to essentially count every rest as an extended rest. Of course if you do this you will have to up the power on all the monsters to compensate. Or is there something else you're looking for?
I would love it if we can come up with a way, in this thread, to migrate daily powers into the ritual system which may cause some changes to the ritual system and the easier task migrate at-will powers into the encounter powers system.
So here is the bottom line:
Let’s make some rules that make daily powers into rituals and make at-will powers encounter powers.
Of course, rituals also have costs like component costs and healing surges, which also don't regenerate after every encounter. So I'm not sure how making daily powers into rituals solves the "limiting factor" problem. I guess I'm still not clear on what you mean by "limiting factor."