Or suspended and never paid?
But I said in my question: "if we suspended mortgage repayments for N months and rental payments for N months"
Landlords are not paying their main cost (the mortgage) so why do landlords go broke? They have some fixed overheads but those are usually a few % of the mortgage.
The mortgage lender was counting on receiving the mortgage payment in May 2020, not in May 2045.
While the default rate increased in some areas, it was in no way universal, or as high as we see today in the retail property market. Also (currently) the property backing the mortgage has retained its mortgaged value. So these are not that similar scenarios
This obviously ignores the issue with massively leveraged firms making poor bets on housing bonds. But lets be real, they'll get bailed out if there's any problem.
Renters stop paying their rent so landlords go broke. Landlords stop paying their mortgages. Mortgage-backed securities go into default. Anyone with lots of exposure to mortgage-backed securities folds. Their counterparties in all sorts of financial arrangements can't collect (insurance, bonds, you name it). Credit markets dry up, and all the Main Street businesses that are rolling over some of their debt find they can't borrow, so they file for bankruptcy. Normally, they'd take out loans to make it through bankruptcy and restructure... but no loans are available, so they liquidate.
EDIT: worth noting that this is less likely now than in '07-'08 because the Federal Reserve has been buying up bonds like crazy (that basically means financial institutions, governments and businesses are often able to get unlimited cheap credit) but if they scaled that back or stopped doing it, things are already so bad there would've been a credit crisis in March or April without a national rent/mortgage freeze. So imagine how much worse it would be with one.