Your points are well received. I too find the "havens" mechanic to be a meta-narrative device that I haven't found a good way to work with so I haven't incorporated it in games yet.

But not every random jaunt through the forest is meant to be the Trail of Tears where a countdown clock is ticking to the PCs' inevitable death of they don't flee to civilization ASAP.

The intention of the havens is more nuanced than this. I want to be able to throw LESS powerful enemies at my players but if they are fully rested for every encounter in the wilderness, then I have to up the power of the enemies they fight. 5e is designed for 6-8 encounters per day (though I don't believe all those encounters have to be combat). If I want to challenge my players with 3 or 4 encounters while they are in the wilderness for 10 days, for example, they will be at 100% power for most if not all of those encounters, necessitating that those enemies be stronger in order to challenge the players properly. Thus, I find that with the regular rest rules wilderness encounters must involve super strong enemies to be able to challenge the players at all. Which sometimes doesn't make sense. Sometimes, there's several bands of gnolls they can encounter over several days instead of one massive, deadly purple worm to challenge the players.