It warms it up, and you're not going to get the absolute maximum battery life out of it if you're wireless, but the impact usually isn't that big, unless you're really cooking it. Using the standard fast charger that comes with your phone is probably going to put about as much, if not more wear than a. 10W wireless charger.

You're not meant to wirelessly charge it by sticking it in the microwave.

Wireless listening absolutely needs more than 2x the power of wired listening. It also needs charging an entire other device

It might be more than that. A wired headset is incredibly simple, unless you're running a ridiculous amplifier through it. It's just two speakers, maybe a microphone and button if it's a mobile headset.

By comparison, wireless listening would usually need the audio encoder/decoder chips, the Bluetooth receiver/transmitter, the processors for the pairing/controls/noise cancellation, and the speakers on top of that. That's not a small amount of componentry.

I’ve tried using wireless charging in a friend’s car on my iPhone SE a few weeks back.

Result: notification that charging had (!) to be stopped at around 50% due to overheating and was poised to continue once the iPhone had cooled down sufficiently. It never continued as that was all I needed to know about the current state of wireless charging with light usage on the side.

Good point on the wireless listening and ear pieces needing a battery as well, though. I guess with those it comes down to convenience for most buyers.