A bit of computer history by Rob Landley:
You know how Ken Thompson and Dennis Ritchie created Unix on a PDP-7 in 1969? Well around 1971 they upgraded to a PDP-11 with a pair of RK05 disk packs (1.5 megabytes each) for storage.
When the operating system grew too big to fit on the first RK05 disk pack (their root filesystem) they let it leak into the second one, which is where all the user home directories lived (which is why the mount was called /usr). They replicated all the OS directories under there (/bin, /sbin, /lib, /tmp…) and wrote files to those new directories because their original disk was out of space.
The /bin vs /usr/bin split (and all the others) is an artifact of this, a 1970’s implementation detail that got carried forward for decades by bureaucrats who never question why they’re doing things. It stopped making any sense before Linux was ever invented.
http://lists.busybox.net/pipermail/busybox/2010-December/074114.html