Unfortunately, it never got past the first line because Nintendo had no online strategy.
Battlefield developer DICE pitched Battlefield as a GameCube exclusive to Nintendo, according to Penny Arcade's Jeff Kalles (and former Nintendo of America employee) on our 2nd Annual Live Podcast Telethon for Child's Play.
Apparently, despite Nintendo's love for the initial pitch, it never got past the gatekeepers because Nintendo had no online strategy in place.
It is worth noting that developers routinely pitch publishers all the time, and Nintendo was likely part of DICE's rounds when they were making Battlefield. Still, imagine if Nintendo had the force of Battlefield to build an online infrastructure around.
You'll be able to hear the whole segment, which featured Kalles, Site Founder Billy Berghammer, Totally Rad Show's Jeff Cannata, and former Planet GameCube staffer Rick Powers, in the next few days.