I think the objective is twofold, really:
First, I think Valve wants to wean users off of Windows. They would love to see a 100% Steam environment on the gaming desktop.
Second, it actually IS cheaper. Look at the cost to buy 2 next-gen consoles with a full load of controllers. It comes out to around $1400-1500 with 4 game pads for each machine, plus things like chargers and online accounts.
With a Steam Box, you're actually spending less money than getting 2 consoles, especially if you consider that PC games tend to sell for $10-15 less than on the consoles. (Not all do, but every game I've bought over the last year has been cheaper on the PC.) Also, look at stuff like Minecraft, which is far superior on the PC than on the console, or Skyrim, which can be modded on the PC but not on the console. There are also all the MMO's, which basically don't exist in the console world.
Anyone who's spent a lot of time with PC's and consoles knows that the PC gaming world is far richer and more powerful than the console world; the only thing the consoles really have in their advantage is convenience.
If you can transfer that convenience to a PC... what's to stop PC's from simply taking over the living room gaming market?