While I agree with the sentiment, a mortgage is collateralised by the house, usually even the starting point is at most 90-95% of the house value (so the loan is in fact over collateralised) and if any repaying took place along the way, even more so. Sure, it's not idiot proof. But government debt is surely mostly uncolalteralised?

The government can always repay by printing currency, but that's not the same. This is sort of a default too, since inflation eats away the artificially repaid debt.