I think another effect of clicker training, specifically free-shaping, is an improvement in confidence in both dog and owner. When the dog realizes that he/she can offer behavior and be rewarded, they will do so, which would be the most visual representation of positive operant conditioning. A creature repeats what is rewarding and can learn or find solutions that are rewarding. In so doing, the dog now realizes a way to reward. When you know something, then there is no question. If I know what I can do and how to do it to achieve the result I want (my reward), then I do so confidently and am generally confident. The same for a dog. In a new situation, they know they can look to you for the lead because you always lead and you always reward when they follow your lead. They are then confident in new situations because they don't have to guard for you or answer challenges, within limits. And that's a reason why it is of paramount importance that an unruly dog be removed from a training class or public scene until some measure of training has been established.
How does work with Shadow, who is Husky in temperment? He is aloof and skiddish when most new people approach, which can be a breed trait. And some scenes are contextual. He is friendly with our neighbor when we walk over there. But when she would check on him when we went to New Jersey, he wouldn't get near her. When she could get in the yard, he would retreat to the far corner. Of course, that was 2 years ago.
By clicking and rewarding for calm behave in a variety of circumstances, it does offer him a possible response to new scenes, such as being calm. I may not get him over his breed's shyness but he also doesn't get as fearful, either. He adopts a wait and see approach. Sometimes, he won't accept a treat from a stranger, at least at the first offering. That's my cue to read the behavior, if necessary. He will take a treat from me in the presence of a stranger. Now, it has translated into him having confidence in me. He doesn't know about these other people but he will look at me.
ETA:
Another side effect of clicker training, including the free-shaping, is the extinction of some unwanted behaviors. Those unwanted behaviors were exhibited before because they were rewarding at the time. Since we strive to not reward the unwanted behaviors and the dog is offering behaviors we do like and reward, they can, at least for a moment, forget about those other behaviors because the ones you want are so rewarding. As time goes by, only the behaviors you want get exhibited because they are always rewarding.