And that's the problem. The game literally cannot be balanced around one recharge for multiple encounters. Because then you cannot avoid the five-minute workday, or whatever new variant pops up. Gamers will wheedle their way into whatever recharge they can to get as much of their resources back as they can before every single fight. That's just what gamers do. Any time period longer than per encounter will inevitably result in the gamers at the table trying to...well...game the system. Hell, even with a per encounter recharge they'll probably try to run away and disengage so they can get a "new encounter" when they re-engage the same enemy.
I don't think it would play out like you hope. Because that requires the gamers at the table to not game the system. That's what gamers do. So they'll hoard their resources until they get to the first fight, nova during that fight, then spend the rest of the session doing whatever they can to not get into another encounter. It might dramatically increase the amount the players actually roleplay, because they'll spend the next three hours roleplaying with every shopkeeper and random NPC they can find...even each other.
To be clear, anything that doesn't take into account the gamers desire to min-max won't work because the gamers will inevitably min-max. Whatever the recharge is, they'll want one full recharge for every fight. At least. Anything less and they'll game whatever that mechanic is to get it.