OP - my instinct is to agree with your point. At a general check-up, I could understand paying the same, but for a specialist visit, I'd be irked to pay a special higher copay and not see the doctor.
I have had 2 completely opposite experiences with NPs. The one at my OB-GYN is fabulous! She takes so much time with me and really seems to understand my concerns, provides lots of info, etc. I don't mind paying the regular copay to see her, because I actually choose her over the doctors now that I've been seeing her for 2 years.
The NP at DD's ped office is another story. She doesn't even seem to be up on current baby/toddler info. At DD's 15mos appt, she only looked at the height/weight percentile, then told me DD was overweight and that I shouldn't give her snacks and needed to switch to lowfat milk.

DD was chubby but not huge, and besides, kids under age 2 are supposed to have 50% of their calories from fat. She didn't ask me what we fed her, or anything - just assumed we were giving her treats and juice all day! We stick to seeing the ped now, who has always considered DD just "healthy."
Like doctors, NPs are individuals, so there are good and bad ones out there. It does seem that in general, NPs are able to take more time to talk to their patients.
To the insurance question, back 10 years ago, my plan had $0 copay for nurse visits and $15 for dr visits. My current plan has $0 copay if you go to a retail clinic (like Target or CVS, always staffed by NPs) but $25 for seeing a doc or NP in an office setting. So there is some precedent for different payments.