Then we can pay them more, or not and they can take another job instead. Either way, I can't take you seriously.
Why not? I've suggested solutions that let them invest without even being aware of what they're invested in or only minimally (index funds, specific portfolios). This resolves the conflict of interest problem while allowing them to still gain the financial benefits of investing some of their money.
Or is the idea that if they choose to work for the government, they need to work until they die.