Yeah, many cities do it, Berkeley just happens to be one I know of because I manage a property there.

The biggest risk is legal -- if you cash two of three checks for example, have you accepted partial rent? Can you evict for non-payment or did you just accept payment? Will the two people who paid fight the eviction? Can you evict just one tenant?

So many thorny issues you just don't want to deal with. So much simpler to say, "give me one check, it's either on time or not".