The error message "The visual studio remote debugger does not support this edition of windows" appears because the remote debugger tries to use Windows Authentication by default, and this is only supported in the "Pro" versions of Windows, and up.
However, the remote debugger does work with the "Home" versions of Windows, you just have to tell it not to use authentication via the command line.
(Why it doesn‘t let you do this after launching it without any arguments, why the error message is so misleading (and contradicts the official list of supported OS), and why there is so little info about this on the web, I don‘t know. :))
To launch it, run this:
msvsmon.exe /noauth /nosecuritywarn
Of course, this launches it in the lowest security mode, so you‘d only want to do this on a secure network. (But that‘s usually the mode one ends up using msvcmon in anyway, as the other mode is an even bigger PITA to set up than it is normally. Very useful tool, but really could use some streamlining.)