* Bad source settings/implementation (i.e. bitrate too low)
* Bad sink implementation/EQ/DAC
* The HSP issue referenced by OP (where you can't have both HQ audio and use the mic)
* FUD by patented codec authors
The reality is that even the basic royalty free Bluetooth SBC codec is perfectly fine, and sounds transparent at high bitrate settings, which decent sources should be using and all sinks are required to support. Transcoding doesn't make much of a difference either. It's a poor codec, but the bitrate is high enough that it doesn't matter. You can ABX test it yourself if you're so inclined, purely in software, with high quality wired audio hardware. I have. You'll see the codec isn't the problem.
So when your Bluetooth device sounds better wired than wireless, or works better with AptX or some other patented nonsense codec - most likely the problem is careless software/firmware (or outright crippling to push patent licenses), not the spec being bad.
(I say this as someone who was gotten into flamewars over the quality of ffmpeg's AAC implementation and found bugs in the Opus reference encoder; I can tell when audio quality drops)