The kernel does not copy every page, but it does have to copy all of the VMAs. Setting memory to COW (which can involve changing a lot of page-table-entries) is not free either. I guess I could have mentioned copy-on-write explicitly, but I do not believe that what I wrote was incorrect.

Fork becomes more and more expensive the higher the RSS of the process, roughly 1ms per 1Gb of the process size with 4kb pages. Given that modern servers can easily support 1-2Tb of RAM the fork() part can easily take several hundred milliseconds, blocking everything in the meantime. So for larger programs you kinda have to have a "fork helper" process if you need to execute external programs for some reason.