For your second point, do you say that you use Adobe or Windows?
Or how about if I said I made this cool image using Linux? More likely I’d say I used GIMP or ImageMagick or some specific command line tool.
Linux is just the kernel. It’s an amazing kernel, but it’s only half the story. The tools on top of it are just as important as the kernel. That’s the point of saying GNU/Linux is to call out the other half of the whole experience.
The reason GNU/Linux isn’t popular to say is that it doesn’t provide any real information. “I run Linux” and “I run GNU/Linux” doesn’t really tell you anything. “I run Debian”, “I run Fedora”, “I run Arch BTW”, those all tell you something different.
I can’t speak to the OS landscape when Linux was released. Maybe saying that you ran GNU/Minix or Bell/Unix or whatever combinations might have existed would have made sense. However at this point it doesn’t.