You can't remove the role playing from the rules or vice versa. No matter how you try to immerse yourself some of the idiosyncrasies will appear. You do have the choice to ignore or just accept it. A DM will have to decide how much effort you want to put into an adventure to address some of the gaps. It is not just a player problem.The more I read of this thread, the more I am convinced that many of the "problems" people have with the game are from a metagaming perspective, and could be alleviated with more immersion--funny enough in a role-playing game.
Here's what I mean by that. I see a lot of anguish around trying to mechanically find the balance of the game, and if balance doesn't happen automatically outside of in-game factors, then the game itself is broken somehow. I am convinced now more than ever that if the players played their PCs like actual people, and the DM played the game world as an actual living game world, most of these issues would resolve themselves. Players using metagame knowledge (I know we'll have X amount of encounters per day so I know I can spend Y amount of resources every encounter) and DMs catering to these players' expectations of rest, refusing to have the inhabitants react like a living creature would to what's going on, and treating monsters/NPCs as pawns on a gameboard with no other actions other than what's in a statblock is going to cause issues. D&D isn't expected to play that way, so if you're expecting the game to do something it isn't designed to do, you'll be disappointed.
Do real life soldiers know how many contacts they'll get on every patrol, so they know exactly how much ammo to use up per contact? Of course not. In the same vein, players shouldn't know how many encounters they will have for certain. Every rest period, short or long, should be a risk v reward evaluation. It's on the players to initiate rests. It's on the DM to fairly determine how every other creature in the area will react. Some times this means PCs get a rest. Sometimes this means the dungeon inhabitants are alerted to the PCs and are out looking for them. There is no manipulation, or cheating, or whatever else has been implied earlier.
Play the game immersive, like a true role-playing game, and many of these issues won't even come up. Yes, this means there is prep time needed by the DM because the DM needs to know how each of these creatures will react and what they would do. That's the price to play when you're running the game. If you cannot, or will not prep for your games, then you have no right to complain the game isn't working for you.
Some days they might have 2 encounters. Some days 10. The average may come out to 6-8, but that doesn't mean you have to have 6-8 every adventuring day. Some days class X will run out of powers before the encounters are done for the day because there isn't a chance to rest, and some days class X will have left over powers because there was only one encounter. That's part of an organic game. The players have the choice in how to manage their resources, rather than have those choices dictated to them via metagaming expectations (which is what "I know I have X amount of encounters so I spend Y amount of resources per encounter" is). It's more player agency.
Probably the biggest issue is the disparity of resource management between classes and monsters. Some are very arbitrary and you would question why they exist.