It's still math and the standardizing to ensure what payroll providers submit is correct is still checked by the government, who could provide said standard.
When things get complex even the payroll providers get it wrong
Where I live (New Zealand) holiday pay got complex, and quite a few civil service payrolls got it wrong (IIRC by a few different providors). It tooke years for anyone to notice, and has taken years, and billions, to put right.
Payroll providers absolutely still get it wrong but not always because it's too hard.
I joke, but a little serious when I say asking bureauracies to get details correct, quickly and consistently might be too much, let alone with software that could threaten jobs and meetings. Canada had a payroll implementation failure in government that received international attention: https://en.wikipedia.org/wiki/Phoenix_pay_system
Having implemented more than I've wanted to - too many are still anchored in the past on a mainframe, abstracted away with a web and/or mobile app.
Still worse, many payroll providers, particularly one of the very largest in Canada, actually still processes payroll according to a "model" that's manually run. It's an excel model, run manually by people. You deal with people directly. Do anything off a beaten path? Guess which model to win.
