You could just light the money on fire instead and get the same result. Contractors routinely screw the tax payer. I once had a job in one of these third parties where the entire operation was effectively defrauding the tax payer by claiming 1hr jobs would take 40.
You are absolutely correct, billable hours are perverse incentives and wrap rates border on predatory, but this status quo is Congressionally mandated and buy commercial as a policy is generally bipartisan.