"Would you lend money to someone who never repaid it and kept asking for more money in perpetuity?"

I certainly would if that person also provided me with the money to lend them. In other words, if they didn't need to borrow and could always simply give the money back with added interest.

The US is a sovereign currency issuer that cannot involuntarily fail to pay any obligation denominated in the currency it creates at will. It is not like any other entity in terms of "affordability", so your analogies to any other circumstance simply don't apply.

"A rising proportion of what we pay in taxes is going only to mandatory spending, fixed payments on programs like Medicare or financial items like the interest on our outstanding debt that must be funded regardless of the health of the country or our economy."

Once again, the household budget analogy is not applicable to the issuer of the currency. In fact, it is the money creation Congress does when it spends that "funds" the purchase of Treasury bonds. One cannot lend what they don't have or doesn't yet exist.

When the proper order of the transaction is realized it becomes obvious that neither taxation or borrowing are "funding" mechanisms for the government, and only serve to draw down the money in circulation in the private sector which would be represented by "shareholder equity" on any corporate balance sheet. In the case of the United States the shareholders are the citizens and the debt represents the accumulated savings from their past productivity, not a mortgage on their future,