They really can.
> this follows straightforwardly from observing how much of the national budget is consumed by debt service as a function of the interest rate.
Decoupling monetary policy decisions from that kind of fiscal concern is a substantial part of the reason for an independent central bank setting monetary policy.
> If they go above five-ish percent, this implies that they'll need to either A) raise taxes to a level that would likely inspire mutiny, B) greatly reduce borderline-impossible-to-cut parts of the budget such as the military industrial complex + welfare spending broadly construed, C) increase productivity by a lot, D) monetize the debt or E) default on the debt.
Note that the first “they” is the Federal Reserve and all the other “theys” refer to Congress.
Also, while government borrowing costs tend to move in roughly the same direction as the fed funds rate, they very much aren’t the same thing and can be very widely separated.