Being serious, I wish I could find one of these 2-3x multiple payouts in government. Every time I've looked at anything government related (including direct contractors) the pay is garbage. Usually 15% to 50% of what the private market pays for my skill set.
The old answer used to be for the government to hire directly, but that's been hamstrung for like 40 years by now.
(Also, OP is probably underestimating the full-sheet cost of a federal FTE, as well as the complexities of fund-based budgeting and forecasting.)
Govt > contractor > sub-contractor > employee was pretty common. I never knew of anyone being a direct contractor to the agency since the contracts were so large and involved a lot of employees.
The actual employer can pay the employed contractor whatever they want, but the rates are published and if they underpay too much the employee will be poached by a competitor. Because the rates are public info the employee can look up how much profit their employer is making any time they want.