2. That invulnerable characters are intrinsically a good thing for the game
I think this is where we'll probably disagree here - characters that become invulnerable, even to a subset of characters - are simply characters who don't actually wish to interact with a certain subset of opponents.
Invulnerable characters are bad for the game in several ways - because as soon as you reach this threshold, there's very little reason to actually interact or play with the enemy team, outside of simply murdering them because they now can do absolutely nothing against you.
While this would be fun for the invulnerable player - this is less of a game, and more of a 'Man, everyone who bought offense is really bad.'
Consider what happens if this is true - if you buy offense, you can't damage a subset of their team - but you can now be murdered by anyone on their team becomes the norm, and under this state - defense is the only real option.