Why pay off all the debt? What are we saving our credit for? Of course the burden can rise so high that it is prohibitive to growth, but in general credit exists to be used.
But for cashflow. There are investments that need to be made that are beyond the bounds of money on hand, not to mention that even if you can afford to pay up front you might deplete your ability to continue other programs services. This is why we have housing loans, credit cards, and car loans. This is commercial paper. this is national debt.
Well, sure. But the reason we don't have "money on hand" to pay for anything is we're servicing all the debt we racked up in previous years.
Over the long term people who pay off their credit cards every month are in a better cash flow position, which is why I laugh when people say they need cards to maintain their standard of living. Countries are no different.
Now, if you're making an investment sometimes it's worth borrowing money. Businesses do that all the time. Governments do it too, but only very rarely, and they usually end up spending far more past the point of diminishing returns.