A user on #emacs brought it to my attention that the xdg-open detection
for browse-url is more complex than it should be and fails detecting
their Linux desktop.  Looking at the definition of
`browse-url-can-use-xdg-open' reveals that it replicates the desktop
environment check as done by `xdg-open` (which is done to detect the
DE-specific default browser setting, not to prevent people not using a
popular desktop environment from using xdg-open).  As enumerating all
possible kinds of Linux desktop is a futile endeavor, I've completely
eliminated this check from it so that the only ones left are whether
we're in a graphical session (by checking $DISPLAY) and whether
`xdg-open` has been found on $PATH.