When cp was invented, 'most filesystems' did not have the first clue about copy on write.
However, I should note that possibly the first company to invent what you describe was Microsoft.
Novell Netware 386 had an NCOPY command which invoked a Netware extension to the DOS API that told the server to perform the entire copy on the server.
But even earlier, OS/2 1.x had a proper DosCopy() system call. Since it could be passed down to the installable filesystem drivers for intra-volume copies, something like the Netware client for OS/2 could in theory turn it into the same protocol call that did server-side copies. There was a NET COPY command in LAN Manager (and LAN Server, if memory serves) that did the same optimization.