OK, this is probably a no brainer but here goes.

When you do a Military challenge and the Defender loses, they get to choose the victim. If they have a character that has a response that Saves the character (e.g. goes back into their hand) can they choose that character?

It would seem that every Marshalling they would be able to play this character and never be in serious danger of getting a character killed. Sure it costs one gold to get that character out there, but then to a certain degree that have a shield.

In this case I am thinking of Viserys Targaryen and his Response: Save Viserys Tagaryen from being killed or discarded from play, then return him to his owner's hand.

Yep, that's how Viserys is meant to be used. He and a few other characters can be used as claim soak: Maester Aemon (who can kneel to save a Night's Watch character, which generally is used to save himself) and Ser Davos Seaworth (whose response allows you to save him, then you have to either pay 1 gold or return him to your hand) are the two other prominent such cards in the Core Set.

You could always play with a lot of 2-claim plots. Or you could do your military challenge, let your opponent save and return Viserys to their hand, then do an intrigue challenge and hope that's the random card that is discarded from hand.

It's strong, but it is also not as broken as it seems when people first encounter it. Certainly, it is not powerful enough to expect a blanket ruling like "if a character can be saved, you have to choose something else to die when you lose a military challenge." A big chunk of this game is expecting to lose challenges, and finding ways to mitigate the damage.