What you can do is give people money to pay rent. But there is no guarantee they will actually use it to pay rent. My guess is that the combination of a moratorium on evictions and giving people rent money would lead to a lot of rental debt accumulating, when what people need to do (if they lost a job due to covid) is reduce their expenses and move to a place they can afford at their new income level, rather than trying to keep staying in an apartment they can no longer afford to live in, waiting for a job to return that is likely to never return.

If everyone did this, rental rates would decline as they would reflect the new levels of income people are actually earning, rather than the levels of income people wish they would still be earning. With the current approach, false price signals are created that make it seem like there is more demand for apartments at a given price point than what people can actually afford, and long term this hurts everyone.