The federal moratorium on evictions only applies to properties that have mortgages underwritten or guaranteed by the Federal government. I believe there are all kinds of conditions on these loans that allow the landlords to defer mortgage payments in these circumstances too.
There is a leverage issue too. Democrat and Republican landlords will be putting pressure on governors to get people back to work.
My son in Ohio has 4 rentals. He is not covered by the moratorium. Rents are coming slowly, but still coming. He pays utilities so if they don’t pay he can’t pay. Not pretty, but it’s a short term problem and the $1200 helped a lot.