The UK does something like this. It's a disaster, because it gives employers an excuse to cut wages knowing that the government will cover the rest - effectively a handout to employers, who don't usually need the money, not to employees, who do.

It's also a disaster because the UK gov is famous for changing payment rules, sometimes retrospectively. The most recent changes leave some of the poorest people owing between a quarter and twice a year's income in supposed overpayments - which they accepted in good faith, with no suspicion that the government would change its mind about them later.

Any tax credit scheme is going to be open to similar abuse - whether accidental, because of incompetence, or deliberate because of political malice.