Your argument might make sense if
a.) GO-TO's programming wasn't broken
b.) GO-TO didn't have a personality
You say GO-TO has never adapted to something outside his programming. So what is his programming? To monitor and advance the Republic's interests by aiding Telos IV.
Nowhere in his original programming did it tell him to leave Telos, create a smuggling ring, get a deadly and cloaked body, set a bounty on Jedi/Sith, join the Exile, go against his allies on Malachor, or make any number of choices. He was not programmed to run a criminal organization.... so how are these feats "ideas to deal with a situation he was programmed for"? Going from an droid overseeing a planet to a criminal overlord seems like a completely new situation to me....
Basically, GO-TO is alive. Droids that gain personalities due to lack of memory wipes are, at least in the mental sense, living. He makes choices on his own accord. His code is broken and he has a personality, along with extensive knowledge. He would be just as good at countering Plaguies's tactics as any other schemeing criminal, if not better.
Well, G0-T0 was one of a series of infrasturcture planning droids. I think they were programmed to take criminal organizations into accout, calculate the impacts of Jedi/Sith, organize interplanetary relations etc. He tried to deal with all those things in the most ressourceful way. But he still acted like an infrastructure planning droid who tries to act in the interest of the republic.
G0-T0's personality actually disliked the Republic, but was still bound to the directive to serve it. Having a personality didn't make it possible to simply abandon his programming. He has to justify breaking one directive with a higher directive.
Also, several other G0-T0 droids "broke". This leads me to believe, this is actually an error in the programming of the entire G0-T0 series.
That doesn't mean Plagueis would find a way to exploit G0-T0's limitations. But it could be possible.