Some people looked carefully at bluetooth for high quality audio - the results were quite variable depending on the implementation of bluetooth on both the sending and receiving device. Latency on some cheap and poorly designed devices was terrible - others were much better. Audio quality also depends on the codec chosen and how the codec is implemented in both the sender and receiver. Again, wide variations in the quality and performance depending on the device. Some common implementations of codecs were incomplete and had serious bugs - in the hardware and software and drivers. Some receiver implementations force the sender to use settings that result in both increased latency and poorer quality audio. Apparently many vendors don’t care about how well things are done if they can still sell things …
That said, it appears that the hearing aid manufacturers that offer MFI devices have attempted to minimize latency. I assume the same is true of non-MFI hearing aid Bluetooth implementations but for them, the hearing aid manufacturer cannot assume that the sender will meet certain specifications as the bluetooth implementations of phones, computers, and add-on bluetooth transmitters vary significantly.
With an open fitting, latency delays the processed signal so it is arrives later than the sound arriving directly. This has been described by some as changing the timbre what you hear. A Siemens paper described the changes as spectral and stated that they attempted to keep the latency in the hearing aid to less than 10 msec from input to the microphones to output of the receiver. Adding fancy processing in hearing aids tends to delay things in the signal processing chain and that information is typically not easily found …
For other applications like streaming TV audio, latency can cause lip sync issues and echos if the latency is long. Some manufacturers like Oticon specify the maximum latency in the processed signal (for example input to the TV Adapter 3 to the output of the hearing aid receiver) but finding the specification or performance may be difficult. Devices like the TV Adapter use both Bluetooth and some other non-bluetooth proprietary protocols in the same basic frequency band - finding out details is difficult, possibly due to the MFI non-disclosure agreements. However for my Oticon OPN S 1 aids and my TV Adapter 3, the maximum latency is specified and is dependent on the input to the adapter: 25 msec for the analog input, 28 msec for the Digital input (TOSLINK), and 45 msec for Dolby Digital (TOSLINK).
In my case, I have a semi-open fitting and I find that listening to the TV is easier if I turn mute the hearing aid microphones so all I hear is the streamed audio. The frequency response is worse, especially at the low end, but I can understand voices better that way. I don’t know if that is due to the latency delaying the hearing aid signal as compared to the signal from the TV sound bar. Maybe the improvement is due to the reduced room noise and reverberations when the mics are muted. Too many variables for me to sort out
One thing to remember for small latencies - there is an increasing latency in the direct signal as the distance from the source increases as sound travels at about 1125 feet/sec so a bit less than 1 msec per foot. If your device has a small latency you can effectively cancel it by choosing your distance from the source.