That's why, just as fork(2) is a primitive for the process creation, copy(2) should've been the primitive for the file creation — creates an exact copy of the file under a new name, but with the exact same content and all of the metadata (except for the name, obviously), including its kind, permissions, timestamps, etc. And no, it wouldn't be prohibitively expensive because all filesystems can quite easily support CoW; after all, most of the created files will be truncate(2)d almost immediately, so there is no point to eagerly duplicate the file contents.
The "metadata is atomically copied" part would support very nicely the usual text editor's idiom of rename(2)ing a temporary file over the source after fully writing it out — you still need to accurately replicate the permissions and extended attributes. And just as shells are important enough programs to have fork(2) almost exactly suited for them, it would make sense to have copy(2), suited for the text editors.
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.
* https://www.edm2.com/index.php/DosCopy_(OS/2_1.x)
* https://www.edm2.com/index.php/FS_COPY