U.s. govt uses tax code to incentive behaviors. We have 1040ez which is almost as simple as the NZ system if citizens don't want or have any deductions.
This really has nothing to do with the topic, every country uses tax codes in that way we just have a simplified system to calculate and pay taxes in other countries
I think the comment has everything to do with it: every time you use the tax code to legislate the behavior and choices of the people, it causes the tax code to become less simple by the very fact that the citizen now has to track that behavior. For example, take charitable donations. Because they're tax deductible, I have to track them, or forfeit the deduction. That's extra, manual work that must be done. Now multiply that out for every behavior that some congressman thinks should be encouraged, and it shouldn't be surprised that the taxes are complicated.
A tax form is essentially a giant function, but one with tons of inputs. It can only be automated once all the inputs are known (essentially, that's the job of tax software). The only person that has all of those inputs is you, so you're forced to buy TurboTax to be able to reasonably input and evaluate taxes.
If you're thinking that all these inputs could ever be tracked by the federal government in a giant database, I still think it's crazy: you'd need a database for student loan interest paid, which every loan organization reports to, for charitable donations, for stock purchases, for stock sales, for dependents, etc. (I don't even know how you'd begin to track dependents, aside from how we do it now: manually.)
Complexity counters incentives, though. Unless the only incentives you care about are the ones available to wealthy individuals and large corporations with tax lawyers. If you burry the incentive in a pile of complicated forms, it's not an efficient incentive anymore.
The 1040EZ has a long list of requirements that can exclude someone from filing with it; including, in some circumstances, those with otherwise simple tax situations (1 job with 1 income).