Walking around with wired headphones plugged into a bluetooth dongle kind of defeats the purpose, no? People buy wireless headphones because they don't want to be encumbered by wires while walking around.
An adapter like that is yet another thing I need to put in my bag, and lacks at least some of the convenience that comes with having headphones that just wirelessly connect to my phone natively.
Plenty of Bluetooth adapters are designed for a specific headphone model and sit flush against the cup without additional wires. When they're attached, it's easy to forget that they're not built in. See https://thebtunes.com/ for example.
A huge caveat is that if the headphones have ANC, you now have two sets of batteries and two power switches to worry about, so they're a lot less seamless.
If you have a good pair of wired headphones it's actually quite a nice compromise, because it lets you use them at home without being stuck in your chair. I'm using a Bluetooth headphone amp right now, it's very light and fits in my pocket, which is more than I can say about my laptop.
An adapter like that is yet another thing I need to put in my bag, and lacks at least some of the convenience that comes with having headphones that just wirelessly connect to my phone natively.