I use Bluetooth headphones almost exclusive at work, home, traveling and gym. Charging them is not an issue for me, as I would much rather charge them than deal with cables -- wrapping, untangling, cable management, plugging and unplugging, etc. Assuming sound quality is sufficient, I'd chose that option every time.
There are a few occasions where wired connections can be more convenient. I made sure my BT headphones have a detachable cable so that I can plug them in when the battery runs out and I can't recharge them. Lag is still an issue occasionally, so when it's critical or badly off, then plugging in is just easier. And sound quality can be misleading, again for critical listening. So it's case specific. Also, the ability to use other BT equipment, and pairing -- in many cases, just plugging in a cable is far easier (Lightning or otherwise).
Generally speaking I think the lack of wire management freedom of movement makes them a much better experience for me.
I'm actually very interested in Apple's AirPods, even though I don't think they're very flattering looking, but if the audio qualities there, the battery solution is pretty compelling -- 15 min charge for 3 more hours; I mean that's pretty reasonable, who can't take a 15 minute break every 3 hours? The issues that remain to be seen are how well they address video lag, but this new W1 chip probably does an excellent job with that. The one issue they haven't addressed is sharing audio connections over BT. And as I mentioned above, pairing is going to be great on Apple products, it's still going to be an issue with anything else. But I suspect as usual Apple has shown the way with this W1 chip, and all BT devices will go down this path quickly.
For $160, I'll probably pass. They certainly seem neat, but I have a feeling most of the engineering went into things like auto on-off and siri rather than sound quality. Hope I'm wrong, because they definitely look interesting. It would be great if they can do all that AND actually sound good.