I very much agree with your sentiment, but I simply don't have any issues with BT headphones on Linux desktops specifically I could work on today.
Bluetooth is a very a complex set of standards - I work as a system architect for a well-known celestial car brand, and implementing Bluetooth and BLE is the bane of our existence; truly disastrous technology - and I'm sure things to improve are aplenty, though. In terms of desktop biz logic, the roll-out and maturation of the PipeWire stack is one ongoing effort to watch for.
What should we support instead? Is there another wireless standard?
I've noticed there are models that use some kind of non-Bluetooth USB dongle for example.
Where do you give money? I've looked into a few projects but it's pretty fragmented. Donating money to Ubuntu was a trip...required digging through forums and finally "Downloading" Ubuntu to trigger the "donate money" pop up.
Linux needs more options for people like me to pay for polish.
It's not just about the money, it's also a way for devs to feel that their work matters.
Indeed, the number of glitches and irritating workaround I have to use to make something else than a mouse work with BT is something most people don't want to put up with their $1000 laptop.
Yes, BT is a shitty tech. But their phone works out of the box. Their Mac OS and Windows as well.
The fact we still get BT not pairing randomly (or wifi stop working, or sleep mode never awaking) is a huge problem in 2021.
We should not ignore that as a community.
That's why I report bugs, give money and help people online.
But it will not be enough if we close our eyes on the work yet to be done.