Do you think that if Barristan hadn't been banned from the Kingsguard he would have beat Sansa when Joffrey ordered him? I'm conflicted about it, because I like Barristan, but I do believe that he would. Just like he didn't do anything with Aerys, I think he wouldn't do anything with Joffrey either. Maybe he would have protested initially, but eventually he would have obeyed his king.
I’m conflicted about this as well. Barristan is the epitome of what a proper knight of the kingsguard should be. Always loyal to the king and to his oaths, he does what he is commanded, he knows it’s not his place to question the king’s orders, but to serve and protect him. Which we know is an inherently flawed mindset. The institutionalized system of honor, oaths and chivalric ideals is rotten to the bone, but Barristan is no Jaime Lannister, he lacks that kind of blind arrogance to actually remove himself from that system that shaped his whole career as a knight. And he probably even lacks the intellectual lucidity to see those flaws critically and be proactive about it. Just like Ned, even if deep inside he knows that the system is corrupt, he just doesn’t have the fiber to openly rebel against it.
But… he is a deeply honorable, just, honest man, and I believe the years spent serving Aerys and being unwillingly complicit in his atrocities left a mark on him, and after his death he promised himself (or at least prayed) he would not serve another tyrant. Robert Baratheon came in; he was a horrible husband and a mostly inept king but hardly a tyrant. Then it’s Joffrey’s turn and he has written ‘psychopath’ all over him. In addition, Joff (and Cersei) show an utter lack of respect for the kingsguard as an institution and a lifetime sacred duty and go as far as humiliating Barristan in front of the whole court because he’s apparently too old to serve as Joff’s royal guard: