Increased complexity doesn't mean lower taxes or higher taxes, in principle, it just means complex taxes.
In practice, it actually leads to higher taxes to pay for an army of people to check the code is being applied correctly.
In Taiwan they have a system where you can choose to do manual deductions (A), if you think that's in your interest. Or you can take (B) 'the average deduction+10%'. Then you have a 1-page declaration of your income, no deductions marked, but they calculate what the guys who use (A) get, take the average, add 10%, then knock that off your tax bill.
No false claims, no evidence to supply, nothing to check, both sides win, each tax official can manage 100x as many Bs as As.
It's a practical example of how simpler tax codes can result in lower taxes by reducing (needlessly) big government.