Is there a technical reason not to do that, or no one else has a use for it ?
No there's no technical reason. It's just not implemented because there was no demand.
Does the remote recycle bin just use a remote move command before the upload ?
I was thinking about how remote recycle bin works, and I put a . in the location settings, tested it, and it created the backup in the same directory.
You are right. That works. I didn't realize that WinSCP can handle relative paths in the recycle bin path.