Have you ABX tested an SBC transcode at the maximum bitpool settings vs the original? Because I have, and I couldn't tell the difference.
The "transcoding is bad" story is about low quality settings, archival, and/or bad encoders. E.g. don't do repeated transcodes with the ffmpeg AAC encoder, not even at 320kbps. But one final transcode with SBC for over-the-air delivery at the max allowed bitrate? That's totally fine, especially for typical Bluetooth use cases (listening on the go, casual headphones, etc).