Interesting observations in this thread. It's got me thinking.
I'm always considering new house rules for my game. Now I think I want to encourage the party to keep adventuring, but to provide some justification for resting.
Maybe I'll do away with the limited healing surges per day, and instead put a cap on the number of surges per encounter. If you want to spend more surges than that during the encounter you can, but you'll take some sort of wound. You only ever need an extended rest for the purpose of recovering from these wounds.
(It's like if you keep pushing yourself to exercise, you can keep going, but you'll be sore, and possibly break something if you're not careful. Maybe you can go over the limit by 1, which lowers your defenses by 2. If you go over the limit by 2, then any critical hit that hits you in the same encounter inflicts a serious wound, like a broken arm or swollen eye.)
Daily Powers instead become Awesome Powers. To use an awesome power you have to spend an action point. You get 1 action point at the start of the first encounter between extended rests, 2 at the start of the 2nd, 3 at the 3rd, and so on. You can't use the same 'awesome power' more than once in the same encounter.
(Maybe at 11th level you get an extra 1 action point per encounter, and an extra 2 at 21st level.)
[Magic item daily powers I don't like in the first place. I'm still not sure what to do with them.]
I think this would encourage players to keep going and build up momentum.