The US pays a very low interest rate on its debt. If you made $250k per year had a 3% interest rate mortgage of $200k, would you pay it off any faster than you had to? Of course not. You'd spend the money on things that would give you a much better return.

There is absolutely no need for the US to pay down inflation. GDP growth will naturally reduce the effective value of the principal. The problem is the run-away increase in the debt over GDP ratio that we've been seeing.