I'm mostly on board with recovering all HP during a long rest. To paraphrase the Hit Points description on p.12, ultimately HP represent the ability to avoid a direct hit that causes injury or trauma that could result in death. After 8 hrs rest, the wounded warrior has recovered from the exhaustion of fighting and the immediate pain of his wounds to the point that he can effectively defend himself for another day. The wound isn't gone, it just doesn't have a game effect.
Hit Points are actually 'Defense Points.' D&D has always resolved attacks in a backwards fashion. The attack roll is actually saying "if the target did nothing to actively defend itself, would this attack penetrate its armor and natural reflexes?" If it 'hits,' the damage actually represents how much skill, luck, and grit it took for the target to avoid a potentially lethal wound.
As others have said, a slower rate of healing is normally hand-waved anyway. "WE leave the dungeon for a day" or "We leave the dungeon for a week" takes the same amount of time to say and resolve at the table.
As far as staying the night in the dungeon, I think the Long Rest rules give enough leeway for the DM to prevent abuse. Those rules state 8 hours of rest, of which 2 hours can be light activity. If the PCs effectively conceal themselves in a dungeon and remain undiscovered, sure let them benefit. BUt if they just bar themselves in a room with monsters growling outside and bashing at the doors... sorry, that does not qualify as a long rest. Have fun fighting your way out now.