I HATE the relationship!!
First, in the federation it is against regulation to have a relationship with a person you supervise - EXACTLY the reason why Spock was sending Uhura to the Farragut. Then to have her blackmail her way onto the ship cheapens BOTH of them. And, had that actually happened, Spock would have immediately ended the relationship it would only be logical.
Relationships are not prohibited on a Star ship - a Spock / Chapel relationship is OK as he is not her direct supervisor.
And of course the line "have I not demonstrated exceptional oral sensitivity" sickens me. It turns Uhura into not much more than a prostitute who is sleeping her way to the top - instead of the reality that was presented in TOS that she was the best damn communications officer in the fleet. It so saddens me that Nichols worked so hard to portray Uhura as both an intelligent black woman - to have jj Abrams movies reverse all of that makes me very sad.
I don't think its illegal in the entire federation to have a relationship with a supervised person.
I'm not certain that Spock ever directly supervised Uhura, no more than he directly supervised Chapel.
Anyway I can imagine doctor/nurses getting into relationships. This sort of thing happens.
Troi and Riker were in some sort of relationship.
I don't think she blackmailed - simply pointed out that she would have got the position based on merit and he had to agree.
Yeh I hate the oral sensitivity and farm animals stuff too. But then again I'm old.
I like that Spock/Uhura are having problems in STID - it would be terribly annoying if they were a power couple all sweetness and light. Then starting to dress alike.