If you buy an X-Box, and the next Halo turns out to suck, you are still going to get your moneys worth of 3rd party titles.
The Wii was designed with different assumptions in mind, which led to a lean machine they could sell at a profit. Someone buying and Xbox and Gears of War was a huge problem for Microsoft, if someone bought a Wii and Mario Kart, it was just fine for Nintendo as long as the customer was happy: Every sale was profit, plain and simple.
I don't know about the Wii not being good for 3rd parties either, it's more that the Wii didn't do what the 3rd parties wanted to do (high tech edgelord games). So we got completely moronic things like a Castlevania fighting game, a Soul Calibur that wasn't a fighting game. How about Dead Space, a slow, ponderous horror title? Yeah, the devs turned it into a rail shooter, just about the most anti-horror genre choice imaginable.
In simple terms, they thought the Wii userbase were morons who would lap up anything - after all, they'd bought a motion control toaster to play technically really simplistic titles, and in the devs' world, technically simplistic = bad. So they gave people disrespectful shovelware, which, surprise surprise, bombed.
They had the opportunity to make solid titles - the Wii may have been a toaster, but it was still beefier than the PS2 or Gamecube which had a lot of really good titles and anyone who's played Metroid Prime knows those controls are crack.
I think the big miss with the Wii wasn't how good/bad it was, but communication. What was the philosophy behind the machine, Nintendo communicating that, the devs really trying to understand that.
You need third parties (sort of) for scaling and long tail reasons, but it's always an uneasy relationship.
If you don't expand enough, or the market doesn't generate a solution, your platform has a gap. If you expand too much, third party developers feel burned and desert your platform.
Microsoft solved this by clearly staking its monetized territory ("the office suite"), and not really expanding in other directions (after those weird 90s attempts).