"I am wrong" is no better a contribution to an argument/discussion than "I am right" is. "I concede" is no better than "I win".
if the arguments are on the table, either everyone already knows you won/lost/whatever, or they disagree about the result, in which case telling them what it is would be dumb.
It seems to me that saying "I am wrong" is a useful thing to say.
Not to advance the argument, but to let the other party know that there's no longer a disagreement and he can stop trying to convince you.
You're right that it has a point generally. That's why I wrote:
"I am wrong" is no better a contribution to an argument/discussion
Your phrase (doesn't advance arg) is clearer, but I did have it.