The debt ceiling is silly IMO, as you said it's been turned into a petty political tool / ploy by both parties.Debt can infinitely increase as long as it comes with increased productivity. The US debt is serviced through new debt since the gov is in a budget deficit. So far it came with increased productivity so there were no problems. What happens when productivity doesn't increase though? You get Japan, Italy, and increasingly the UK, at major economies.
This debt ceiling thing is an issue because it is a legal limit only the congress can increase. It becoming material for petty politics shows how dysfunctional and self-harming US domestic politics are. The US govt can't borrow without the congress increasing that limit so it can't service existing bonds. If the US defaults on even a tiny percentage of its debt, it would be really harmful to the USA. US bond interest rates would increase permanently to account for the increased risks with the US bonds, which would in long term cost trillions of USDs to the USA. In short term its effects would be more drastic. The US economy would contract this year.
All of this would happen because of Republicans vetoing the lifting of debt ceiling, effectively banning the US Govt from servicing its debts.
As for the sustainability of the ever increasing debts, that's made possible by the USD being the reserve currency, which is due to the size of the US economy, the petrol dollar status, and the military might of the US, not much to do with productivity at all IMHO.
I still assert that the chickens will soon come home to roost for the US.