Sure, but that makes all the difference. I often work on an embedded remote machine with quite restricted vim (can't use a custom config, particularly no language packages). When I am on the remote machine (typically I have to run local commands), I often discover I have to edit a python file (typically just minor edits). So to use vim sftp://host/path/to/file I have to open a new terminal copy the path and then open using sftp. For me that interrupts enough of the workflow, that I just don't bother and instead just edit the file on the remote machine using the restricted vim.
Can you install bcvi on that remote machine? (Genuine question - when I've been in similar situations, it also would have been a no-go to install a binary.
It depends, compiled binaries, no. If it's a shell script yes. Python or Perl maybe. But I agree ideally it would work by transferring a script (or aliases ...) across the ssh link and remove it afterwards.