Why does DC always end up with the ten year interest rate?

I have the ten year treasury rate and the effective federal rate. The effective federal rate is the current interest expenses divided by the total public debt.  I have scale factor to convert both to a proportion, (% value times 100).

But the maturity structure, the distribution of loans by term has changed from four years to six years, and varied in between.  Yet regardless, the market always assumes the government should pay the ten year rate.  Why? A new puzzle.

The possible answer is the 30 year mortgage rate for home loans is set to the ten year, and if that is a large part of the economy, that would set the peak of the distribution, other rates would be set in the -pLog(p) sense.  That number is 5% of the economy, not enough, it seems to me.

DC runs on the eight year recession cycle, but that is not all.  There is also the 30 year secular stagnation cycle, the cycle that is driving DC to bankruptcy.  The market may be charging DC the ten year rate to offset the cost of the secular stags it is causing.  This would be the extra fee the debt cartel charges treasury.  How often is the census? Every ten years. What happens at each census? Increased mal-proportionality in government flow, more inefficiency.