I'm not saying that I don't understand the filesystem. I'm used to it, and I often forget how random and silly it is. My point is that if you try to look at it with fresh eyes, it is a bit silly.
And people tend to do what you've just done, which is to make up an order and arrangement that almost makes sense. But the truth is, the whole thing evolved over time, and almost none of those things were the original intention. As someone pointed out, /usr started out as the place for user home/profile directories, but people kept putting things in there that didn't belong, which lead to the creation of /home and the abandonment of /usr to "another place we put binaries, for some reason."
AFAIK, /var started out as a place for specifically variable-sized files. The idea was that if you had a set of files which might grow very quickly, you might want those on their own drive or partition so they wouldn't overrun the rest of the system. Now, when you get down to it, it's because sort of like the /home directory that doesn't belong to any particular user. Sort of like Windows "ProgramData" folder. And /etc was named that because it was a bit of a catch-all for anything else, but really now it's pretty much a dedicated "system configuration file" location.
But those are just the names, and my point wasn't just "Oh, I don't particularly care for the names". My point was, this is a structure that's grown organically over decades, and it is not really "clean". Do we really need /lib, /var/lib, and /usr/lib? Do we really need /bin, /sbin, /usr/bin, /usr/local/bin, and /usr/sbin? My impression is that some of this repetition was created as a bit of a kludgey way to solve some particular problem, and then left in place for compatibility/legacy reasons, and maybe just "we're not sure whether this will break anything, so let's leave it alone." And then, after sitting around that way for a decade, everyone was so used to it that it just seems like "the way it's supposed to be."
And fine, whatever. It works. People are used to it. Why change for the sake of change? But don't pretend like it was an elegant planned organization.