Whenever I'm getting a blowout, they do dry it all the way and then straighten -- but I haven't done that in over a year! I've been going to more curl-focused salons. At my DEVA cut, she dried it most of the way but it was still slightly damp when I left. I was okay with it, though. I have massive amounts of hair, so diffusing it entirely would probably take hours and leave lots of frizz! My non-Deva but also curl-loving stylist does a similar thing, he pretty much dried my hair to the point where it was about... halfway done? Mostly dry up at the roots, and not drippy. I was fine with it, my hair dried completely in about an hour and a half.
I generally think stylists are hesitant to dry curly hair completely because it can cause frizz or it just takes way too long.