Worked for a govt contractor years ago and I would imagine the payout from the govt contract was at least 2-3x. There were usually 2-3 layers of people getting paid and I don't think any of them were hurting. Of course no employee was getting a massive payout compared to private.
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.
It's been several years since I've done contracting work (and for the FAA no less), but that can't really happen to the extent you're implying. The open roles for contract positions specify a pay range based on experience (degrees and/or years of experience). You can have a prime and then a sub contractor, but the amount that each can add for management overhead is limited and depends on the contract vehicle. I want to say it was around 5-10%.
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.
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.