[Oroboro]

Kirito is a nice person who likes to help other people when they're in trouble.
Kirito is not a ruthless pragmatist who will use others and sacrifice them for his own personal gain.

This all comes back to that age old argument of "Do the ends justify the means?" Maybe you think that the situation of "Vague chance his wife might be in the game" should take precedence over absolutely everything else, but Kirito as a character obviously prefers not to compromise his own moral code, or burden / hurt others with his own personal issues.