Correct me if I'm wrong but isn't there an inherent vicious cycle in that if the price gets too high our ability to pay it off becomes uncertain, at which point the premium for the risk would shoot up dramatically (and so on)?
The yield increase is basically the market pricing in the interest rate increases since they're expected now.
Given the wealth distribution of the population has become so unequal, raising taxes for the purposes of lowering the deficit is a politically impossible option. So the only politically feasible option is controlling spending.
I'd like you to spell out your thought process, because I completely disagree with the relationship between your given and your conclusion, and I'd like to know what you're thinking.
It is generally accepted a wealth tax will not directly meaningfully lower the deficit. There's also examples of those who would be affected spending massive sums of money lobbying against such taxes and threatening capital flight. These are generally the same group of people as political donors.
Studies also show 84% of people across the top 36 major countries believe wealth inequality is a problem in their country. This leads me to draw the conclusion that politically popular tax policy and wealth inequality are closely intertwined.
All these things considered, a political party evaluating the risk of policy changes on their polling would always pick the option of reducing spending.
Government debt yields on the short end are set by the Fed. Long yields are "set by the market" based on inflation fears, and mostly guessing what the Fed will set rates to over the next 10+ years.
Japan had way higher Debt-to-GDP for decades, yet the long term yields were low. Why? The central bank said "we anticipate yields to be set low for a long time" and did so for a long time. Recently they said they are going to "respond to inflation" like all other central banks and suprise, surprise the long end is creeping up. "Bond vigilantes" came into existence as soon as the central bank changed their policy.
It is possible to break this cycle, but it requires getting spending under control. As long as you operate in deficit, it requires finding private capital to finance future operations of the government. That private capital will require interest commensurate with the expected future devaluation of its principal to lend; otherwise they are just suckers. If you can bring spending into balance then you can hike rates and bring inflation under control and you'll be somewhat insulated from what bond purchasers are willing to accept, but if you can't then increases in rates just increase government spending as well.
Japan operated at extremely high levels of debt-to-GDP because their deflationary trap turned all major Japanese corporations into large net savers. Why would you hold debt when you have to pay it back in more valuable yen in the future? That created a very large oversupply of private capital, which crowded into government bonds as the spender of last resort.