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.
You seem to be under the impression that the government itself doesn't have the same problem. Government agencies often over bill, over budget. They have an incentive to pad everything and to never lower costs because their budget will be lowered otherwise. Contractors on the other hand, have to compete with other contractors so while they can try to over bill, if they bill too much the government has an incentive to switch contractors.
Neither system is perfect.