X-Men's mutant powers. Invulnerability always sounds great, but the setbacks are rarely considered until they actually manifest as a problem. These problems are usually the result of extenuating circumstances. But for superheroes and superheroines, such things really should be thought of ahead of time, because the idea of "extenuating circumstances" comes with the territory.
With their ability to super self-heal, the biggest extenuating circumstance for Wolverine or Daken is being put in a situation where either of them is immobilized and isolated. If they're stuck somewhere and they can't die, their only hope of release is if someone finds them. And if someone doesn't, then they just spend forever stuck in one spot unable to change their circumstances. Even then, maybe that doesn't sound so bad until the idea of "forever stuck in one spot" really sets in, and, invulnerability aside, there's only so much a mind can take, superhero or not. Worse still is if the cause of their immobilization is something excruciating.
This horrible scenario comes to in X-Factor #7, written by Leah Williams with art by David Baldeón. After a mission tailing Siryn goes awry, Daken is impaled and stuck somewhere no one's able to find him right away. It's days before Northstar eventually does find him. Befoe that Daken is left healing around the thing impaling him, but unable to move, and unable to die. If just a few days drove him crazy enough to say later that he wished he'd just died in those few days, just imagine how he would have been if he'd been stuck there longer. Granted, his father Wolverine probably would have done better, but then he's been through the wringer with his healing factor more, having been bombed, pulled underwater, and imprisoned, all with full awareness that he was stuck in those places without being able to look to death as an out to the madness he would have been driven to.
So as handy overall as it is to have invulnerability, clearly there are some flaws to it. The most prominent being stuck in a situation where death is the only out from otherwise existing meaninglessly in one spot with no hope of moving from it. And yet, for this flaw, it opens up a lot of poignant meditations on death, most interestingly, why it's important that living things can die and why being unable to is so unnatural and undesirable (despite the comic book trope of characters being able to come back to life all the time). Like with most superpowers, many readers and fans may fantasize over the idea of having them, and invulnerability that extends effectively to immortality is certainly one of the most appealing. But this flaw in it reinforces the importance of understanding how futile it is to have the power to cheat death so easily.
Moreover, it gives the opportunity for unique reflections on life and mortality. That Daken comes out of his situation wishing he could have died when he'd only been stuck impaled until Northstar found him in just a matter of a few days is telling of not just his character specifically, but of any character who might have been in that same situation. Even for Wolverine, who has dealt with the issues much longer than Daken, this fate would likely be unbearable. In this context, death is seen as a relief that was out of reach, the true salvation, as supposed to any more thoughts of being rescued and returning to living a normal life. Or at least as normal as life can be for of the X-Men and X-Factor. So, as they say, just be careful what you wish for.