Hello Shabnam,
This is a nice example of a policy that targets a social determinant of health (money) but clearly could have huge health benefits. The issues you raise about evaluation are critical - another issue is that a rigorous RCT would be very expensive. Because the treatment is actual money, it is going to cost a lot more than most treatments. Some of the best evaluations available though are for WIC and EITC programs, which use variations in program generosity as natural experiments. You might check out the NAM report we wrote on health disparities:
https://nam.edu/addressing-social-determinants-of-health-and-health-disparities-a-vital-direction-for-health-and-health-care/
where we discussed this type of program. Among social policies for health improvement, this is actually an area with relatively good evidence.
Maria