The price doesn't fall because the future purchasing power falls, the price falls because there are better alternatives in the market. No one will pay $1000 for a 2% return when they can pay $1000 for a 5% return. Market participants will always maximize their return. Bond prices adjust to be competitive or equivalent.
But the govt. doesn't have this problem. They don't care about maximizing return - they care about containing contagion. So they can pay $1000 for a 2% return and not still not lose money over the long term.
Inflation strongly determines interest rates. You are getting 5% return because inflation expectations are high which caused the Fed to raise interest rates. When you see 5% risk free, you assume high inflation. The price falls because of the risk free rate, which is caused by high inflation, which causes drop in purchasing power.
But the govt. doesn't have this problem. They don't care about maximizing return - they care about containing contagion. So they can pay $1000 for a 2% return and not still not lose money over the long term.