I’ve long wondered about this question, now there is a paper about it, from Johannes Abeler and Simon Jäger, forthcoming, “Complex Tax Incentives,” American Economic Journal: Economic Policy. The abstract is here:
How does tax complexity affect people’s reaction to tax changes? To answer this question, we conduct an experiment in which subjects work for a piece rate and face taxes. One treatment features a simple, the other a complex tax system. The payoff-maximizing output level and the incentives around this optimum are, however, identical across treatments. We introduce the same sequence of additional taxes in both treatments. Subjects in the complex treatment underreact to new taxes; some ignore new taxes entirely. The underreaction is stronger for subjects with lower cognitive ability. Contrary to predictions from models of rational inattention, subjects are equally likely to ignore large or small incentive changes.
I would think the real world danger is that intermediaries will teach people how to game complex tax systems over time. Still, the actual tax incentive faced by individuals may not be so transparent even to informed and strategic advisors, nor are the advisors always able to communicate actionable advice to the individuals facing the taxes.