If we're assuming that the government is evil and sufficiently organized, then it seems much more likely that they would want to calculate taxes themselves. They could make a lot of money just by "accidentally" introducing a few errors.
Only if the aggregate impact of those errors is lower than the aggregate impact of the overpayment mistakes that people make when the file their own taxes. The latter also offers much more in the way of plausible deniability.
This is American politics. The politicians say one thing to please the masses and do exactly the opposite. I'm not trying to be confrontational or rude. That's just the reality of things.