the government would withhold the taxes and you got to say ``okay'' as opposed to following the rules at the end of the year to find out how much you actually owed.

Still sounds like PAYE. Except that, in the UK, your employer is responsible for working it out and sending the money to the taxman (usually monthly), rather than the government arbitrarily taking the money.

This bothers me because the government regularly withholds absurdly incorrect taxes from my paycheck.

Now that I can understand being a concern. In the UK, if the taxman screws up, he'll give the money back at the end of the year, or adjust your tax code so that you pay more next year.