Part of the problem is random bureaucrats have no way of knowing if Joe Schmoe's Web Shop can actually do the job. Some of it has to also be covering your ass - if there are serious flaws in the system, your ass is covered if you spent $350 million - not so much if you spent $450k.

I have no idea how the process goes, but it seems like some sort of outside consultation on picking appropriate bids might help. Maybe even something like the congressional budget office, but for software systems. That way expertise can be concentrated and they can focus on their core competency, rather than requiring every agency to develop people who can properly analyze bids for software systems.