In the meantime: Would it be difficult to create a "Bluetooth send" application, maybe combined with "Browse remote device"?

It's still not as good as integration in the file manager, but it would get the job done. Start application, select file, select device, send. (could even be a desktop widget,)

BTW: Is it only "Send to" thats missing or also the ability to browse BT-devices?

Oh, yes: I voted of course.