Yes. Five minutes to heal someone with magic? Sure, why not - it's magic. A five minute breather and some bandages to completely come back from a blow that sent you unconscious, bleeding, within an inch of death? Nope.
I don't reject it out of hand, I reject it because it wrecks my suspension of disbelief. I don't have a problem with characters being able to heal themselves, as long as they are able to use a plot device that makes sense according to the story. As problematic as potions, wands, and healing magic are, at least they offer a plausible explanation in this make-believe game. Binding one's wounds, catching one's breath, etc., are all fine and good for bar fights---but without the benefit of magic, how does one suddenly explain how the guy who was burned half-to-death by dragon fire ten minutes ago is able to calmly and painlessly press onward as if nothing had happened?
It is perfectly fine to say that the 4E damage and recovery mechanics don't make a lot of sense with regards to characters who were just kicked to the threshold of death's door. Honestly, they don't. Of course, they never have for any edition of D&D. But, I'd argue this is a problem of D&D's classically terrible death and dying rules, and not a problem with hit points and healing surges.
I mean, if you really look at it, mechanically speaking D&D characters are never really killed by injuries, because hit point damage never really models injuries very well. There is no point on the HP damage scale where characters suffer broken bones, get cut tendons, lose limbs, lose an eye, etc. Instead, HP works such that a character falls unconscious when HP reaches 0. It is fundamentally a form of tracking
non-lethal damage (which is why subdual damage was conceptually redundant). If anything, it models the amount of pain a character is suffering from rather than the amount of injury they have suffered.
Really, the weird thing about D&D is that, rather than dying from an injury, characters seem to just spontaneously die of heart attacks due to excessive pain. Characters
never suffer fatal injuries. They instead just suffer a bizarre form of pain-induced unconsciousness that directly leads to death. As a whole, their bodies never suffer the negative effects that would be associated with actual injury. Of course, this is a problem for
all editions, not just 4E. This is why the idea that HP damage is equivalent to physical wounds has never, and will never, make sense.
Within the context of what hit points actually model (pain and fatigue, with the result of zero HP being unconsciousness), healing surges make tons of sense. They work great as a system of healing that form of damage. The fact that they don't model lethal injuries well is merely a symptom of the fact that HP damage doesn't model lethal injuries well, and not a problem of the healing surge system itself.
I'd much rather see 5E create a system that makes severe injury and death more realistic, interesting, and fun, rather than see healing surges be sacrificed on the altar of trying to turn HP damage into something it is not.