Good idea. If you're interested in this type of thing, check out 18F, which is a brand-new engineering office run from within the government in San Francisco and DC: https://18f.gsa.gov/
One important dynamic is that contracting, due to its slippery nature, attracts the kind of people whose skill is siphoning money away from government while minimizing what they deliver.
Think about it: Even contracted physical construction gets screwed up in large scale government projects, and building good contracts about software development is much harder that contracts about physical construction.
In-house development simply doesn't have the kind of indirection where the bloodsuckers can get in.
You'll cut one kind of bloodsucker out of the loop and let another in: the kind that thrives building fiefdoms in bureaucracies.
And you're not addressing the main issue: projects being way too big and unwieldy (if now somewhat less expensive) even before they go over budget, over time or flatly fails altogether.
If the CGIs of the world actually delivered a functional product on time and on schedule, the fact that they earn handsomely in the process is at best a secondary concern. Next to the cost of the staggering embarrassment that was the failure of the first Obamacare website, whatever CGI quoted is a rounding error.
It's incredibly difficult. When government money is involved the good old boy network swings into action. Contractors are picked based on political connections first and actual capabilities second.
I wouldn't be so cynical. Contracts are really awarded to companies that can jump through the bureaucratic hoops--and there's an entire industry dedicated to doing that while over-charging and under-delivering.