I think Bluetooth could similarly be useful for e.g. heart rate monitoring apps for sports.
As the op commented, why not leaving the burden of managing/pairing the heart rate monitoring device to the OS? In the same way audio and input devices work? The only real use case that comes to my mind with Bluetooth support is indeed monitoring, but it’s not about heart rate.
I mean, why not also use it for controlling a LEGO robot from a Scratch app? Configuring presets of your coffee maker without needing a mobile app? Updating the firmware of your soldering iron via vendor web page?
Just providing supervised access to Bluetooth LE would satisfy these all without adding custom interface for all current and all future devices we might want a web page to interact with.