2) Batteries are inconvenient
Title says it all: having yet another battery to charge is, in my professional opinion, an unacceptable pain in the ass.
Why on earth would you limit yourself that way, especially with the main instrument you use in situations like an airplane? You might find yourself without access to power, and welp: you’re outta luck. Sorry about that! While battery tech is getting better, there’s always that point where a cell will stop charging. When that happens, you need to be able to change out the battery—but not all headphones allow that. At this point, your headphones are dead.
Unless your headphones have an active noise-cancelling unit, this isn’t an issue for wired models.