User Profile

Is there any way to stream audio data from wireless mic device to iOS device via classic Bluetooth (which requires MFi program)? I'm currently think of SPP, but the data rate might be too slow to stream 16bits audio data. I'm wondering if it works or is there a better solution/profile for streaming audio data to iOS device?

I've currently received a task that requires to evaluate the possibility, as title, of recording via mic on BLE headset and play sound via built-in speaker at same time on iOS. I've done implementing forcing audio device set to built-in speaker whenever the BLE headset is connected/disconnected. It works if both mic/speaker need to be set to built-in one. But after days of search and try, I found that it is not possible to make mic/speaker set separately. Even specifying input device on AVAudioEngine is supported only on MacOS, not iOS. Can anyone or any technician give me a persuading answer about "Possibility of record via mic on BLE headset and play sound via built-in speaker at same time"?