The third session of our PF2 playtest is tonight and we might be able to finish the first part. We've rested twice, both times because of a mix of consumed healing resources and simply hitting the end of the play period. IIRC, the Cleric has been focused on healing, though they did get into melee last time, got roughed up, and had to withdraw. We definitely experience the X-minute adventuring day, limited by healing.
As the Wizard, I cast my first meaningful spell in the second session and had lived off of cantrips up to that point. The Wizard has the luxury of cantrips that contribute to combat. The Cleric does not have a healing cantrip. While that might solve the X-minute day I would find it weird. It would make the game seem more like the old "Gauntlet" video game. ("Elf shot the food!") Yet, for reasons of being a flawed and inconsistent human, I've always been okay with folks acquiring CLW wands to bring along. Just shoot me.
Really, the x-minute day thing is more a result of adventure design. If you feel like you have to fill out a dungeon with a selection of creative, yet filler, encounters, then you have fights that don't necessarily contribute to the story and drain resources, forcing the party to stop exploring the story.
In a sense, skill systems have trampled on some roleplay. In D&D 1e, for instance, there was no skill system. If you wanted to search a room you did that through description. "I check the desk drawer for traps. If I don't find any, I look inside." Then the DM would cough up what was in the drawer. Searching a room might take several minutes of play. These days, "we search the room." One set of rolls and you get a list of stuff. You're done in a minute. Next room.