I was using Unix long before Linux came along, and you're right it was the fork that pushed the most for the desktop. Even though today I am using it as my desktop that's really only because I write server software. I think the main thrust for Unix on the desktop was in fact OS/X, but among us geeks it has been Ubuntu. But that was really my point, it was the distros like RH and Ubuntu that put together something installable with a mostly workable window manager that most people associate with Linux, not the kernel.
While I am very much not taking anything away from the work that Linus has accomplished, my point was that much of the credit for today's Linux installations comes more from RedHat than anything Linux did in the kernel.
There indeed was the BSD wars, but most of the old timers that started their career with a flavor of Unix (for me, it was HP-UX on an HP9000), since then they have all been much of a muchness, varying only in their applicability to a given problem (including suitability to the desktop.)
I am reasonably sure that the number of Linux desktops is very small, nearly every practical use for Linux is running servers. I would wager that OSX dwarfs Linux in terms of unix-on-the-desktop comparisons.
Since history provides no A/B testing capabilities, it's very difficult to isolate the impact Linux has had. Would we today be all using some form of BSD, or maybe Solaris/Intel with ZFS. Who knows, but I am thankful to Linus for a number of things including his efforts to promote OSS.