I haven't read a legitimate argument against the IRS calculating taxes automatically, but here it is.
The more invisible taxes are to the individual person, the less they think about that money (and the higher taxes can go without them complaining too much).
Rent feels expensive because every month you write a check for rent. However, for many people, taxes are a much bigger expense than rent. But taxes don't feel as painful, because people don't write a check every month for taxes. Taxes are just invisibly withdrawn from your paycheck.
The easier and more invisible it is to pay taxes, the more you forget about how much money that really is. If you believe in constrained government, there's a good case to be made that we should make tax payments more visible, not less.