I do know what the cost of enforcement of individual income tax is, at least in a sane system with effective witholding and most people not submitting stupid tax returns every year: about 1.25% of money raised (https://publications.parliament.uk/pa/cm201012/cmselect/cmtr..., table 7).
And the simpler you make the system the cheaper it is (this is NOT flat rates - calculating graduated taxes on income is basically free) - you can see this from the "National Insurance Contributions" line on the same table, which is an effectively zero-complexity additional income tax which costs a third of a percentage point of money raised.
So not astronomical. Really quite efficient.