Yeah, it's entirely possible there wouldn't be any therapists left. But I think that even if there were one, or even just someone who was good at talking to people, they'd be snaffled by Galactica to keep the pilots on an even(ish) keel.
But yeah, it wouldn't exactly make for good TV! Unless the therapist turned out to be a cylon, or to have some other kind of weird agenda, but they already kinda did that with Brother Whatshisname and the Chief, so that would be boring.
I think Kara is a fascinating character, and a lot of that is her broken-ness. But ye gods sometimes it's traumatic, watching her hurt herself and other people. Ouchypants.