But maybe iOS just uses the built-in microphone more often to avoid having to switch away from (high quality) unidirectional audio on Bluetooth?
On the standards side, there's Bluetooth LE audio, which also offers very low latency, but that might actually require hardware changes (I believe there's reliance on some hardware layer changes).
However I can't really answer OP question. I am not sure how iPhone get a better sound quality if what OP is saying is true (I don't have an iPhone). What I know is that in Linux you can activate mSBC and this improves the quality a lot when using HFP profile, but it is still significantly worse than anything A2DP has to offer. I also think Android uses mSBC if available, but I am not completely sure.
[1]: https://en.wikipedia.org/wiki/List_of_Bluetooth_profiles