"And so Mozilla has to compete with IE6 which will eventually make Firefox better and in the end the web wins"
That is exactly what happened. That's how Firefox was born if you remember. IE6 was dominant and Firefox rose from Netscape's ashes to challenge it and it turned out to be a very good thing.
Indeed and has lead to much greater cross browser support for standards, it ain't perfect but it's a lot better now. Even IE7 was a breath of fresh air and that was practically forced by the competition from FF, Op and the like.
That is exactly what happened. That's how Firefox was born if you remember. IE6 was dominant and Firefox rose from Netscape's ashes to challenge it and it turned out to be a very good thing.