You asked if we could make the same argument about Arya being a bad person as Dany, given their acts. I said she is an assassin, and she kills people based on her training as a Faceless Man. Faceless Men serve a specific function in Westeros society, so her role (eventually) was as a protagonist, we just didn't know what she was a protagonist for. Many fans hoped those skills would play a role in Arya helping save the good guys, but that was never clearly shown aside from Walter Frey, so it didn't go anywhere.

Dany also had an earned path. And she ended up going mad at the end, as telegraphed. Both Arya and Dany were earned development, and both were protagonists, but for some reason people object to what Dany became. I can only assume that some people viewed her as more of an empowered female character and were blinded to what was actually going on.