Why should I divide into separate file systems?

Several reasons.

Upgrades

You want to be able to do upgrades or reinstalls and leave some filesystems untouched. This remains a valid reason for separating certain areas from others, but with the speed and capacity of modern backup systems, it is hardly as compelling as it used to be.

Fsck

You want to be able to clean the filesystem in the event of a crash. Older large filesystems took a long time to clean and fsck needed more memory than was likely to be present, so it would need scratch files, which slowed it down further. It was not at all unusual for these filesystems to get confused for no particular reason; not from a crash, just because, so it was obviously better to clean one or two small filesystems now and then as opposed to having to clean one big filesystem every time this happened. Linux ext2 filesystems still have that mentality, btw, and will automatically run fsck after x number of boots and/or x number of days. Older Sun filesystems would run it on EVERY boot. Modern filesystems very seldom need to run fsck anyway, so this is not an issue.

Partial drive failure

You want to contain the damage. On older systems, it was often observed that if you had physical or electronic damage, it was sometimes unrecoverable by fsck, but that it was very apt to be confined to one filesystem. Therefore, spreading the filesystems out made it more likely that more of your data survived a crash. Again, this is unlikely to be an issue with modern filesystems, and as we tend to back up more data more often from and to more reliable media, it's even less important.

Space:

You want to control how much data gets put on a drive. For example, in some environments, I'll make /var/spool/lp/temp a small filesystem of its own. This causes it to fill up if there are too many unfulfilled print jobs, which calls attention to the problem before it really gets out of hand and fills up something more important. The idea here is that it's better not to print than not to work at all.

A similar concept might apply to temporary directories, but keep in mind that the booting system is apt to need those too, particularly /tmp and possibly even /usr/tmp, so those need to be available during boot and in single user mode.