Hunkering down isn’t always an option. You’re making a lot of assumptions about a given situation. There are situations where it may be more or less impossible to make a fire (and of course, situations where you don’t want to make a fire because you don’t want to be found), and where you will die, and fast. Or where no one really knows you’re lost, so there’s no reason to expect “dudes in the air” looking for you.
Of course, in a lot of extreme conditions, you’ll probably be dead no matter what you do. If you’re somehow lost in the wilderness in a place that is very, very cold, and you have no way of attaining shelter or fire–then you’re dead. I mean, trying to get back to civilization is really your only hope if fire/shelter are completely ruled out, but realistically you’re going to freeze to death fairly quickly.
Even in the best case scenario where you can hunker down for awhile, live relatively comfortably off the land and keep a fire going, after a week or so most rescue efforts have probably died down. There’s no guarantees you’re going to be found, “shit happens” maybe for some reason rescuers who are looking for you think you’re in a vastly different stretch of wilderness than you actually are or et cetera. Just in my experience from watching the news after about two weeks search and rescue is pretty much exponentially decreased as everyone probably considers you dead, and it is a lot less urgent from the perspective of rescuers when they think they’re looking for a corpse (which won’t go anywhere) versus a living person who needs saved.
I agree there’s never really any reason to do the acrobatics Bear Grylls does. Most of the time in nature, no stream/river/etc is lacking in some relatively safe, natural areas to cross. There’s few situations when climb down sheer cliff walls or crawling across a precarious fallen tree to cross a raging rapids is remotely a good idea. Any injury you sustain in the wilderness will probably be fatal if it has any chance of getting seriously infected or it leads to limited mobility. But, hunkering down can’t always be your only game plan, you have to have something else on the plate.