I'd say there's two types of "intentional" complexity. There's the complexity that comes about because we feel like some actions should receive preferred tax treatment over others. So, tax expenditures like student loan and mortgage interest deductions and so on. They had some complexity because "we", as a government, decide to do that.

But the darker side is the complexity that exists to let people with enough income and the means to obfuscate their true tax rate. We may have a top marginal rate of 39.6%, but even people who have a huge income pay nothing close to that. And it's in high income people's interest to keep it that way. It's also in the interest of the companies we're talking about to keep the tax code complex both because they're run by high income people and if the general population has a sense that the tax code is super complex for themselves, they're more likely to use tax preparers even if they actually have very simple taxes or just mildly complex.

So, yes, with a huge economy the tax code is going to be very complex. That's just politics and the nature of the beast, but there's more complexity than there needs to be because of interests who drive it to complexity for their deadweight gain and strive to keep it complex.