You'd need to consider the balance of including utility dailies or not. I think you'd have to exclude them or you would create a balance issue between daily utils and encounter utils.
You'd also have to make sure all the characters have the standard AEDU setup. If you have Essentials or Psionics in there, it's going to be tough to come up with a system that balances well with all setups.
All that aside, it would create odd restrictions on what you can do as a DM. You can't put the big boss fight at the start of the day, because the players will want to use their dailies.
If your goal is to extend the adventuring day, you will probably get about one extra encounter out of this setup. Healing surges tend to be the bigger day-ender in my experience. Maybe each milestone you get a daily refreshed OR one (or two) healing surges. Even better, a number that scales related to how many surges you start the day with. 1/4 max surges rounded down, or 1/6, or something.