David, I partially agree with you that the quality of most BT headphones is a significant problem and very good BT phones like yours or Senn Momentums or B&O's sound very good. I do own what you would consider the headphones of my dreams, your dreams or most people's dreams. And yes, they cost considerably (!!!) more than your Bose wireless. Lucky me. I also use high end earbuds with my iPhone, which similarly cost way more than your Bose headphones, they sound great, deep delineated bass, musical instrument accuracy, impressive sound staging, the whole 9 metres even.
BT is a transmission protocol but says nothing about how music is compressed to be sent over it. Early BT music devices (transmission and receiving) used a compression codec known as SBC which was not designed to sound good, and it doesn't. SBC was designed to be low power. Hence cheapie headphones/buds using this codec (how the music is compressed) are at best no better than 128K mp3s. i.e., they suck.
Standard BT specs also allows for other compression codecs including Apple's AAC, MP3 and ATRAC. Most higher end BT headphones and buds support these codecs though its rarely clear if they always do. More recently a private company, CSR, came out with the AptX codec which they claim is able to still compress music over BT but to CD quality. In order to use this AptX codec the company using it has to pay a license fee to CSR which means both the device sending the AptX codec and the headphone/buds which receive them have to each pay CSR for the privilege. Some Android phones do, some higher end BT headphones also support it. To work, AptX has to broadcast and be received by AptX devices.
While Apple pays to use the AptX codec for Macs they don't for iOS, perhaps because of the vast number of iOS devices relative to Macs, I don't know for sure if this is their thinking. Apple uses its own AAC compression codec over BT from iOS devices. Like MP3, AAC can be used at various levels of compression. AAC compression is better than MP3 compression so for example, in general, AAC 256k is about the same quality as 320K on MP3. The higher the number the better the sound but the more bandwidth that's needed to broadcast the BT signal. As an aside, Apple music is compressed to 256K AAC on best quality (and you only get a similar quality over Spotify if you pay for their premium service, otherwise Spotify uses much heavier compression on their free level.). There is an even newer high fidelity compression codec out for BT but again its proprietary and you need devices which are able to both broadcast and receive this codec which means manufacturers have to pay to include them. As most people don't know about this stuff and and generally haven't until recently cared, most headphone companies and most smartphones avoid these relatively esoteric codecs to keep their costs down and we've been stuck with cheap crappy BT SBC headphones/buds.
AirPlay on the other hand uses a lossless codec, the music isn't compressed at all. While you need relatively good earphones/buds to hear the difference, you don't have to be an audiophile, you only need to be able to compare like for like. Because BT has to now been used for sports earbuds or by people commuting on buses, trains, and cars, there hasn't been a demand for better quality. Most BT transmissions with decent earbuds are fine when you're running or on a subway train where there's a lot of ambient noise. But these days more and more people are using headphones with noise cancelation or earbuds with sound isolating tips and they can hear a difference between crap, better, really good and excellent. Any lossy compression is going to sound less good than lossless compression although high end lossy (AAC 320K or Og Vorbis 320k, etc) is very close.
With Apple dropping the headphone jack and offering only lightening headphone/bud connections (a problem for people who want to use their earphones/buds with their macs or other music devices and for people with higher end plug in headphones/buds) I think Apple are hoping to shift people to wireless. No more tangled wires, no more wires catching on coats, branches, etc. BT which as I described only broadcasts with lossy compression, hence my question about AirPlay headphones since Apple already has AirPlay built into iOS devices.