SSH is not primarily used to copy files. It's used to log in to and operate remote machines/server via a secure link, and create secure tunnels between hosts. It's available (or can be installed) on pretty much all the main operating systems out there.
SSHFS is limited to remote mounting, available only on systems that have FUSE available - it doesn't serve the same purpose. scp isn't really complicated, it has similar syntax to its "predecessor" rcp. If all you need is to copy one or two files, scp is just fine. You might also be interested in sftp.