If / or /var run out of space (even now) then lots of daemons get into quite a bit of trouble. Anything from hanging to consuming a lot of CPU in the disk allocator.
It's often not possible to ssh into a machine where / or /var has filled up.
There was also the problem of file system robustness. Whilst things were a lot better than the non-UNIX platforms of the day, things weren't quite as good as they are today. These filesystems often were not journalled. That meant that if you had a power failure you could lose the entire volume. (I've personally had at least one / partition be destroyed by fsck after a power failure. I was so, so glad I didn't lose /home. /opt and /usr/local as well!)
Depending on whether you were the user or the administrator dictates which partition you prefer to survive, but at least it adds some robustness. It's nice to have things separated based on how you will restore them. / and /usr will come from the vendor. /opt will probably be a whole load of different media from all over the place.