If we can just choose to rest whenever we want then Strahd doesn't seem very powerful as we can just walk around like we own the place.
This is true especially for the horror genre. I'm not necessarily saying that resting without fear does drive tension, though.
Mainly, its the fear of facing something that may be stronger than you and you can't just back down. Its knowing that they have some tricks up their sleeves and not knowing if what you have will be able to completely handle those tricks.
Take any FPS game, rarely does the term "resource management" get used to describe them. Play through it with infinite ammo or mod it so ammo drops give you 2-3x the ammo(if not more) and you will have a very different experience. Not only that but the relative value & advantages/disadvantages of the various weapons is going to be thrown out the window in many cases. 5e creates this same situation by erroneously targeting resource allotments to an absurd standard of 6-8 combat encounters that wotc's own adventures themselves don't even pretend they are trying to meet it.
Well, this analogy kinda falls flat for me in that FPS games have always been more about skill for me. Sure, ammunition is limited but I definitely don't remember the hardest parts about FPS's being how much ammunition I have. Its usually a balance.
I think a better analogy would be turn-based JRPGs as they're directly related to resource management without timing or skill hurting your overall gameplay.
But, actually, when I play JRPGs, its rare that the tensest moments are when I have low resources going into a fight. Those are usually just random encounters where if I get too close, I'll backtrack to the healing location.
In JRPGs, the hardest fights are boss fights and its never walk into those without full resources, yet a good and balanced JRPG will have me struggle regardless. Why? Because its usually managing turns and buffs/debuffs. Sure, I may run out of MP in the fight a few times but I will have plenty of MP recovery items so that resource in itself is still somewhat plentiful if need be.
I find myself in trouble when I have to do multiple things but only have so few actions. This usually occurs when one or more team members go down. Should I revive or should I press their weaknesses? Should I buff/defend against an incoming attack or try for an ailment to prevent action? Should I debuff or heal? These are the tension driving moments.
If I go to a boss fight without 100% resources, or close to it, I'd be frustrated especially at the random encounters and I'd consider it an overall negative experience. Having my resources drained isn't a fun experience especially since its before a fight where you know you should have as much as you possibly can.