We have a similar thing in the US (section 8). The program is intended for low income people. The affordable housing programs I'm mentioning aim to help people

We have a similar thing in the US (section 8). The program is intended for low income people. The affordable housing programs I'm mentioning aim to help people at roughly the median income afford expensive areas to ensure income diversity. Cash based methods can significantly hurt that goal as such people generally would be better off living in a cheaper area anyway. Or the program handles subsidies building by building which seems administratively complex.