In one important sense, there is a "bubble" in US government bonds, and we should be worried about it.
There is always something normative in saying that the price of something is above the fundamental value, so that people are paying "too high" a price, more than they "should", more than its "real value". I want to make that normative element explicit.
If the US and world economy were operating as it should be, with expected and actual inflation higher than it is, expected and actual real growth higher than it is, and the expected and actual return to investment in real assets higher and safer than it is, the price of government bonds would be lower than it is. And the price of real assets (like houses) would be higher than it is.
I approach the question of "fundamental value" as a macroeconomist, not a microeconomist -- from a general equilibrium, not partial equilibrium perspective. If we define the "fundamental" value of an asset as the price that asset would have if all markets, not just the market for that asset, were in long-run equilibrium (and with inflation at target), then bond prices are above their fundamental values. And if we define "bubble" as a price above that fundamental value, then bond prices are a bubble.
A bubble in house prices is a bad thing. It will cause over-investment in building new houses, under-investment in other things, and under-consumption. A bubble in bond prices is a much worse thing. It will cause under-investment in everything, and under-consumption in everything, because it causes under-employment of everything. That's because bonds and money are close substitutes. A bubble in bonds causes a bubble in money. And a bubble in money can cause a bubble in bonds. Or perhaps they are just different aspects of the same bubble, in both money and bonds.
It's not the bubble in bonds per se that is the big problem. If there were only a bubble in bonds, and no bubble in money, it would be no worse than a bubble in houses. It might lead to the wrong mix of real investment and consumption (presumably too little real investment and too much consumption, due to a wealth effect). It's when a bubble in bonds spills over into a bubble in money, the medium of exchange, that we get a big problem. An excess demand for the medium of exchange is what causes, and is the only thing that can cause, a general glut of all goods. And that causes employment and output to fall, and both consumption and investment to fall.
That's why we should be worried about the bond bubble.
If the US and world economy returned immediately to long-run equilibrium, and expected and actual inflation increased to target, the price of US government bonds would immediately fall. And people who held bonds would suffer a large loss when the bubble burst. But perhaps it won't return to long-run equilibrium for a long time. That is what holders of bonds must be forecasting, because if they are right in this forecast, their decisions to hold bonds at current prices are rational.
And maybe they are right. Who am I to know better? But, like all bubbles, the beliefs that sustain the bond bubble are, at least partly, self-fulfilling. The bond bubble, and the associated money bubble, create the general glut, and prevent the economy returning to long-run equilibrium. And the belief that the economy will not return soon to long-run equilibrium is what sustains the bond bubble.
We need to burst the bond bubble. Bursting the bond bubble will help the economy recover more quickly.