Showing a regulatory taking is very hard, there isn’t much chance unless the regulation hurts the value of the land by at least half. Don’t think apartment complexes in LA are down half in value, or even 5%, solely because of this regulation.
The part that a tenant can pay late and then not repay for a year is a stronger case for the landlords. That’s changing a contract signed by both parties solely and drastically in one party’s favor. The cities and states very much can regulate rental contracts with rules like this, but whether they can retroactively on existing leases is a much harder question.
Emergency powers during a pandemic is a powerful argument. However, the law isn’t limited to evictions because of pandemic job losses, e.g., a movie theater employee. Further, it seems like this isn’t directly about the pandemic, but the second order economic effects. The cost of the pandemic is being shifting to and heavily concentrated upon one discrete group.
This all seems like anti-landlord overkill. Already, as a practical matter, evictions were stopped for months because of court closures, and the remaining ones will take even longer than normal. The law needlessly hits landlords even harder than this, with seemingly no benefit for public health.
This is also about LA being cheap: they want to help impacted households who can’t afford the rent, but rather than provide assistance with public funds, they are just dictating rent is free. That in theory it can be collected later is for practical purposes meaningless in most cases, because most tenants are judgment proof.