In my opinion the heaviest users of Sims are people who are trying to push theorycraft in unique directions. For example, there was a time in WotLK where frost DK's were using a spec that was colloquially called the "machine gun" spec. It was based around spamming Icy Touch as much as possible. A lot of people questioned this, but they simmed the everlasting crap out of it, and along with logs, they found that it was actually optimal for that time.

Blizzard of course did not intent for DK's to play like that, so they fixed DK's pretty quick so that couldn't happen.

Also things like unholy dual-wielding. That is still being tested and simmed even now.

Usually you don't need a sim (in my opinion) when you have a relatively standard thing going on. It's only when you want to do something outside the box, like use a spellpower MH weapon for enhance shaman. Or again back in wrath, when people were talking about armor penetration caps, simming also helped there.

The other thing you'd try a sim on is using a certain ability with different stacks. Like, say as an ele shaman, you want to see what your DPS would be if you hit earth shock at 5 stacks of lightning shield, instead of 6. Or maybe 8 stacks. Or if you are a CP class, using abilities at less than 5 cps. Things like that.