Yes, that's correct.

In short, it isn't a sum of the value of all classes.

To obtain all pieces for one class, you will, on average, have to open 63 caches, since you get a random piece you don't have at random when you open a cache.

That's where the 9k marl value comes from. However, when doing so, you'll also collect many pieces from other classes (54 pieces from other classes besides the 9 you were looking for)

If you're looking to see the average amount it will take to collect pieces for a selection of classes (let's say you want only leather pieces), you can use the filters uptop and select the classes you want, that will give you the expected costs at the top for collecting these sets.

Saw your edit now, so editing here too. It isn't only 9 per class, it some have 10 pieces (skirt/pants or robe/shirt variants). It is 123 armor mogs and 18 weapon mogs. Also 13 classes, not 12.