Similarly, I assume that gem cutting is just removing the areas with decent gems
You should read into what gem cutting and facets really are. There's a lot of skill involved in working out the best angles to cut the stones on in order to waste as little as possible and still get bright shiny stones. There's also a lot of skill involved in cutting them.
I actually am well acquainted with the subject. My point was that INSIDE DWARF FORTRESS what's "really" happening when you perform a gem-cutting operation is the dwarf walks over, pulls out a chisel and hammer, and gets out a couple of chunks of rock which have nice bits in.
This is the logical consequence of "cut gems" having no quality modifier.
Now, once you apply the gems to a floodgate or something like that, a jeweler is actually going to take a look at these now-handleable pieces of rock with gem in, and decide what to do with them. This is when the actual faceting and setting takes place. A dabbling jeweler will just, I dunno, glue on little of the gemstone randomly, or decide to tumble an opal, or do some other stupid thing like wire-wrapping a fifth of a carat of faceted agate. The decoration will still end up making whatever it's attached to look a little better, but it'll be a waste of a perfectly good gem.
A legendary jeweler, on the other hand, could do a hearts and arrows cut by hand, and put the diamond in
exactly the perfect spot to bring out its natural brilliance and blah blah blah I don't actually like diamonds that much.
Point is, as the game currently treats them, the "gem cutting job" doesn't correspond with how gem cutting actually works, so "gem setting" has to pick up the slack. If "gem cutting" actually resulted in gems with quality levels, I wouldn't be making this argument.