Given what a software engineer could make in the Valley/at a FAANG, how much would a software engineer need to be paid to take a government job that banned them from working at a FAANG[M] for the next 10 years?
To make that prospect even money for someone qualified to work at a FAANG, the signing bonus for the government job would need to be in the millions (which obviously won't happen).
I'm only one sample, but I will not work for FAANG so long as I can manage not doing so. One reason I didn't move to SV a while back is that I concluded once factoring in CoL, I'd be taking a pay-cut working anywhere but FAANG. Where I live is cheaper than SV, and NoVA is cheaper yet, so competitive pay in that area would be not too terrible.
I tried to work for the government. It was a 60% pay cut and a demotion - I did quite well in my career so I didn't have the years of experience required to come in at my current level because that's how the government evaluates employees. Plus stunted salary growth. And this was for a government job that has a special salary exemption 'to be competitive with the market'.
No matter how much money the government has from taxes, there is no way in hell they are going to pay enough to be competitive with FAANG. It's anathema to government culture (unless it's for a football coach). You have to let people go back to FAANG to recoup those losses or the government will never be able to hire anyone.