Last trip, I got to Hollywood Studios very early (6:10). They let us through the tapstiles up to the next point at 6:15, but when they opened the park to Toy Story Land at 6:30 (!), I stayed behind to enjoy the nearly empty park (I had a later FP at Slinky Dog).
I asked a photographer at the corner of Hollywood and Sunset to take my picture by the fountain. She chatted with me about how she had nothing to do, with everyone moving up to TSL. Then she told me to sit facing one way and then the other--I now have one picture of me with Mickey and one with Minnie. So cute!
But my overall experience has been that of PPs: sometimes I have had to ask, especially if there's one I know I want, and fewer times the photographer has done it on his or her own. It's best to have the ones you really want in mind and ask for them, rather than leave it to chance.