While I don't think that's a bad idea in some situations, it means trusting the case worker with access to the entire account (as they could use the recovery email to reset the password). It's also an extra burden to put on the case worker, and the individual who has to coordinate with the case worker.

Additionally, this only exists in some magical, fantastical world where the unhoused only have one case worker. In reality the unhoused bounce between a patchwork of government and non-profit services, and because of the soul-crushing workload and emotional labor of those jobs the individuals in each role are also subject to frequent turnover. So the only way this would work is an account that's shared between everyone who might work with that unhoused client at each organization (there are often multiple handling different aspects such as housing, mental health, money for groceries, etc.), and as clients move geographically or do other things that make them eligible or ineligible for each organization's services, that recovery account would also need to change or transition to some new org. Even a single recovery email address is just a totally unworkable solution for the reality they face.