Again, I think this is a pretty major leap in logic. I'll agree > Barristan may have been depressed but what evidence is there that he didn't oppose the inclusion of Blount or Trant in the KG? It's not up to Selmy to decide who gets in the KG.

If Cersei Lannister could pass over the likes of Richard Horpe and Jon Arryn could appoint Mandon Moore, do you really think that the most honorable guy in the Kingsguard out of the original seven, the guy who added the most luster and respectability to Robert's cause couldn't have said something, vetoeed someone or suggested another?

I'm not sure what point you're trying to make here. That Barristan is anti-Baratheon and pro-Targ? That he was never fully invested in protecting Robert? Because your example of him being unable to protect Robert from the boar is completely unfair in my opinion. Lancel had already filled Robert with strong wine and the boar was just a happy accident. In fact Varys even says:

So he says, so he says. But the blame overall for the events that led to Robert's death in part lie with Barristan, as they do with Eddard, Stannis, Jon Arryn, and even Robert himself etc... He failed him with the boar, and he failed him at court.

Yes, I recall Jaime recounting Aerys' raping Rhaella and Selmy standing guard. But unfortunately, I don't think this constitutes him breaking his vows. Yes, this behavior is abhorrent. But it's not for Selmy to step in. I'm confused about this point as well. What about this behavior is so awful from Selmy?

Some of the knighting ceremony:

"In the name of the Warrior I charge you to be brave." "In the name of the Father I charge you to be just." "In the name of the Mother I charge you to defend the young and innocent." "In the name of the Maid I charge you to protect all women....

Tell me, how well did Barristan uphold those last two? How well did any of the Kingsguard, including Jaime up until he slew Aerys (and even then, you know, Elia and her kids...)?