The pay thing is completely irrelevant and again just suggests your real complaint is a turf war. But you're talking to someone with 14 years of post college education (MD+PhD+residency+fellowship) who makes a salary in the bottom 5% of all psychiatrists, by choice. What do I care what anybody else makes? I'm happy with my life. There's no way an NP could do my job. But also, no NP would want my salary.
The independence thing is also totally irrelevant. I don't want to have to supervise some other professional. I have enough BS on my plate.
My only concern, again, would be safety issues. The most commonly used psych meds are relatively benign, with little in the way of serious side effects or drug interactions. It's fine with me if psychologists want to prescribe SSRIs. It's better care to see one mental health provider than two.
Lithium? Clozapine? Anyone stupid enough to want to prescribe those without going through med school and psych residency should not be treating patients in any capacity. Other MDs won't even prescribe them, just like I wouldn't prescribe digoxin or methotrexate.
NP is a whole nother issue and again, the concern is safety. You can actually find old posts of mine on this site where I argue that NPs fill a need given the shortage of psychiatrists. I don't think I understood at that time how thin their training really is. I've seen some very concerning medical decisions since then that make me extremely wary of the whole NP thing.
Psychologists prescribing SSRIs would actually be safer than NP, because about the worst thing you can do with an SSRI is give it to someone with undiagnosed bipolar disorder, and a psychologist would be way better at figuring that out than an NP.