There are a number of problems with this idea.
1. The consoles are made by different companies than the games. The xbox is made by microsoft, the PS3 is made by Sony, and the Wii is made by nintendo, however gmaes for these systems are made by hundreds of third party developers.
2. These days consoles do a lot more than just play games. Ok, well this isn't exactly true for the Nintendo Wii, but the PS3 is also a blueray player, and can access the internet, and both the PS3 and the Xbox 360 get netflix, and on demand movies which you can buy. These are no longer just game machines, they are full entertainment systems, and they are bought for more than just to play games.
3. This would only make sense for hardcore players, those people who buy tons of games. This is how World of Warcraft works, the game itself is incredibly cheap, or even free in some cases, but they make the bulk of their money from the subscriptions. This means that the more people play, the more they pay. Sadly, this doesn't work the same way for consoles, where after you buy a certain game, you can play it as much as you want. Most of the people on the escapist buy and play a lot of different games, but there are many out there who only have 4 or 5 titles, and are content with them, which would end up losing money for the companies providing the free consoles.
4. When people buy used games, the money from the sale of the game goes directly to the retailer, and not to the developer, or publisher. If games became more expensive by $10 or $20 to make up for free consoles, people would actually buy a lot more used games, which would lose the developers more money, and would not recoup the loses from giving away free game systems by the manufacturers.
The way the current videogame market works, the OP's idea cannot be profitably supported.