Alrighty. Here's my two cents (as a client AND as a stylist.)

As a client I have never ever had a hairstylist successfully do my hair to my liking. I've had a few do a decent job but it was rare for me to not immediately go home, wash my hair and start over. Only once have I had a stylist ask if I wanted it styled at all (and that was a huge fiasco in general) and one stylist gave me the option to have it blown out straight which I occasionally accepted because it is a huge pain to do myself.

As a stylist, I would only assume that my client wants to be styled-- unless they request not to which does happen. Finishing IS part of the service but I find that when styling a curly, I have to do a much more in depth consultation just to dry them than I ever would for a traditional blowout simply because I can make no assumptions about how their hair will react.

I also have huge limitations on what I can do because of the product lines I have at my disposal. I work at a large salon which carries 5 very high end brands and none of them work like the products available here. So when I style a curly, I just have to make an educated guess at what will get us closest to the end result we want and wing it.

I will say that as a stylist with curly hair myself, I have a huge advantage over straight haired but more experienced stylists. I think of how long it took me to figure out how to do my own hair and, quite frankly, I can't imagine having to figure that out on another person randomly over and over with different hair each time.

Strangely enough, the majority of the curlies who come in have no clue what they're doing anyway and when I show them some basic tricks, it kind of blows their minds. When I mention this website as a resource, it blows their minds. I say this only to point out that most stylists are probably not used to (#1) doing curly hair and (#2) being expected to do it correctly (i.e. how WE as curlies do it.)

I think I'm getting rambly.
If your stylist can't blow your hair out straight, that's just ridiculous. There's no reason for a competent stylist to not be able to take you from curly to straight (and without a flatiron.) That's just basic stuff.
Mid-back length 3a, red.
Currently using: Joico, Redken, LA Looks Curl Look gel, BRHG.