Mainframes are not slow. IBM's POWER architecture has some downsides but it is no slouch in transactions/second.

> payments taking over a day to go through

That's due to the protocol. https://en.wikipedia.org/wiki/ACH_Network "when a real-time transfer is required, a wire transfer using a system such as the Federal Reserve's Fedwire is employed instead".

> people not being able to receive unemployment

That's probably not due to the mainframes. https://slate.com/technology/2020/04/new-jersey-unemployment... That's probably an administration issue. https://www.citylab.com/equity/2020/04/unemployment-benefits...