Strong first party and strong third party coexisting hasn't happened since the 16bit days. Third parties want weak 1st party, because they are generally scared of competition. It's just hard as hell to go up against any strong publisher month in and month out. If Squarenix was publishing monthly or every other month, you might see other third parties bail from the console Squareenix is pushing. Big, well known titles vs You sucks for You, as a dev. EA is a bit of a different beast, because they mainly produce two types of software: Sports and Fastfood Software. Fastfood software lasts about a week, so it's not a big threat and sports is an oversized niche really.
For Nintendo, they lost 3rd parties and their userbase lost faith in those third parties. So when those companies came back, and some with weak efforts, they didn't gain back that trust. Generally, you look a monthly release list and you know Nintendo generally delivers. Others are questionable. Capcom is the only company that comes with effort on every console they develop for.
For MS, they'll live by 3rd party because it weakens Sony.
For Sony, they tried to be Nintendo without being as strong software wise as Nintendo.
Though, if you're going to challenge a strong 1st party you got to be smart with releases. Too often I see companies release their big titles right next to major 1st party releases and then watch as it gets overlooked. For the Wii, October was pretty wide open for a 3rd party to take the gut of sales. Granted, Halo 3 is the big release of the general time frame, but the Halo audience and Wii audience may not really steal from each other. The only company taking advantage of this is Rockstar with Table Tennis and Manhunt both in October. Capcom is releasing Zack n Wiki in October, which is mart considering its niche factor, but a game like Umbrella Chronicles could have really shone in October. Instead, Capcom is releasing it right after Mario Galaxy, which is going to devour sales.