1. batteries run out and can't use until recharged. Even if that only took 10 minutes I wanted to use my headphone now, not later.
2. batteries die and are not replaceable. Bad for both pocketbook and the environment
3. interference can make them unusable. Try walking through a crowded train station and you'll find you get about 2 seconds of audio for every 5 seconds of nothing.
1 step forward (no wires) 3 steps back.
1. No wire randomly snagging on door handles and other objects.
2. No forgetting your phone is on the table when getting up and yanking it off the table with the wire.
3. You can switch the source with a click, e.g. if you're listening to music on your phone and want to watch something on your computer.
4. It doesn't really matter where the source is: while having a meeting on your computer you can seamlessly get up and make yourself some tea while you keep talking and listening.
5. No physical connection to erode. Maybe I'm doing something terrible, but I've had issues with the headphone jack with nearly every phone I've had and nearly every headphones I've owned. It wears out, somehow.
It's well worth it for me, but I can't speak for anyone else obviously.
The fact is performance wise wired headphones are still just better, as well as far cheaper for audio quality.