I really don't understand why HFP is still the industry standard. Even devices within the same ecosystem, like MacBook / iPhone / AirPods seems to use it based on the audio quality. Or maybe it's AVRCP. Sounds horrible either way.
AVRCP is the control protocol for BT media (e.g. when you volume up or play/pause from your headset). I’m assuming you meant A2DP which is the protocol for receiving audio. HFP is totally separate from A2DP in that it’s a bidirectional audio stream. That bidirectionality is the difficult part - you have in theory tight time bounds for transmitting the data for latency reasons + these cheapo headsets have 1 radio which means they’re nominally limited to tx or rx. Since the assumption for the design is voice calls, you severely clip the microphone audio into the frequency band for speech & transmit mono which is why the audio quality is so bad (+ you further lossy encode it but the frequency reduction is probably the biggest dip). All of this has to fit on top of the PHY packet transport that time-divides access to the channel + has to coex with other 2.4 GHZ radios like WiFi (at least historically).
Now, could these designs be revisited? Probably. Maybe radios are small and cheap enough that we should have 2 and a protocol for bidirectional audio that allows independent streams over separate bands with software synchronizing and mixing audio. It’s also possible the audio encoders/decoders could be modernized with more modern compression techniques to improve audio quality without requiring changes to the bandwidth allocation. Bluetooth those is very ossified and the standards bodies move like molasses - most of the investment is in WiFi and radio vendors are more interested in milking what exists now (or coming up with proprietary solutions like aptx) than actually solving the problems.
BLE Audio supports bidirectional audio up to ±1300kbps ("2Mbps" but with overhead subtracted) which is a LOT better than HFP, especially with LC3 as a replacement for the older codecs.
I don't think many devices support it yet, but the spec has a perfectly acceptable bitrate for modern audio calls. We just need to wait for hardware vendors to pick up on BT5.1 features. Last I read about these I think the focus for BLE audio was on hearing aids and such, but there's no reason the spec couldn't be used for headphones.
BLE audio also allows for things like connecting your headphones to multiple sources and broadcasting audio to multiple receivers. The standard has improved significantly, but without cheap, mass produced chips, these advancements will probably be stuck in expensive purpose-built devices for a while.
Best hack I've come up with when I have to use Bluetooth headsets on calls is to use them unidirectionally by selecting my MacBook microphone as input (try option click on volume control in menu bar).
Just get a wireless headset that uses a USB dongle. It's archaic but it works. I can't stand to be tethered to my desk when I talk. It's annoying and silly how I have a BT headset and a USB-wireless headset on my desk at the same time and I switch depending on whether the call is coming over the phone or the PC, and theoretically I could get one device that does both with a switch (eg. my wife has a Logitech one that does that) but this approach works for me.
I've literally gotten a compliment or two on how great the audio is when I'm doing remote presentations, but maybe that's because I often privately grouse about people who are using awful mic setups and so somebody was watching for that. I'm not using anything fancy, I just buy upper-mid-range gaming headsets (the $150US-ish ones that are good-enough that they don't cover them in neon plastic and LED lighting).
At least for Xbox controllers and headsets (and logitech lightspeed mouses too) they don't use bluetooth, they use a proprietary protocol, you can connect them using bluetooth but if you really want low latency you will need a proprietary dongle.
I suppose sony do something similar, and as far as I know they all use the 2.4GHz band.
Good thing both Xbox and Playstation controllers have a 3.5mm jack and I don't need to buy their overpriced shitty headsets to play without significant audio latency.
There are simply no common successors to HFP. There are a few handsets that use two A2DP streams, but that requires a lot of bandwidth and I don't think support is anywhere close to universal.
Bluetooth 5.2 adds BLE Audio which offers more flexibility. The LC3 codec is supported by Windows 11, Android 13, and Linux, and it significantly improves audio quality compared to the older codecs. I'm not so sure about hardware support in headphones, though.