I hear you, and agree that if it's badly done, it's ... badly done.
To me, the 'making it work' is what makes the stories great.
I love the internal struggles to be 'more than' human and not interfere with the rest of the ship. I also enjoy the protocol-rationalizing that happens, reminding them of their Starfleet duties first and foremost, facing situation in which one may have to leave the other in a dangerous situation, or send/be sent to die. Just the day to day professionalism of not seeming to play favourites can make for a good read.
Some fanfic is nothing more than words on a screen, created out of love for these fictional characters. Love doesn't necessarily equal talent, however, and there are some fanfics that don't compel me to read past a few lines.
Some fanfic is absolutely stupendous; those that are well-written and fully explore many different aspects of the humanity (Klingonity? Vulcanity? Borgity? Talaxianity?) which includes emotional needs are true keepers, in my book (pun intended). I love the struggles and the race/chase more than the catch/win, more often than not for epi-add-ons. Endgame fixers (my fave) carry on after that, and the catch/win can proceed in many, many ways.
*off to search for some links*