Systems (normally) model organizational processes, so companies with garbage processes usually have garbage systems in place too.
This highly specific case reeks of fraud, and you should be able to report them to some kind of ombudsman so you could get your couple days' worth of fees back.
Contracts by definition cannot bind people into illegal conditions, and there's degrees of neglect that can be considered illegal. The entire point of an ombudsman is to keep actors within "this is not illegal" lines; I'm guessing you could do this on small claims court too, but with the plague and everything it can take a lot longer