The simplest tax code is either a flat tax, or a progressive tax with no deductions. Wait, do I mean no deductions, even for charitable contributions?! Yes, that's what I mean, and you begin to see my point about why tax reform is hard. Some complexity will be preserved. The political question becomes this: which complexities get preserved? Some deductions are just too politically popular to eliminate. Consider the home mortgage deduction. Take that away and plenty of homeowners will complain. But, does it serve a valuable economic purpose? That is more questionable, particularly after an economic collapse caused, at least to some extent, by too many people buying houses they couldn't afford.
Then there are the less popular but more economically important complexities, like the tax benefits for long-term investments. Capital gains are taxed at lower rates if you hold an asset for longer than a year. So, buy some stocks, hold them for longer than a year, sell them, and you pay a pretty low tax rate on what you make in profit. To a lot of people, particularly on the money-hating left, this sounds horrible, but not only does it encourage investment, it encourages a healthier form of investment than the high-frequency traders who cause a lot of the real problems in the market. This is one of those attempts to create market distortions that are beneficial, even if you need to understand some economics to see how.
The problem for debating tax reform, then, is about how to decide which complexities to keep. That's hard, and every group getting a benefit thinks that theirs is critical. Everybody in Congress represents different kinds of groups. When they are unable to agree on whose benefits are kept, what happens?
Congress defaults to minor changes at best to the existing tax code, which retains its complexity.
Doing tax reform requires making tradeoffs. You can't give everyone everything. Keeping it revenue-neutral so that it is tax reform, and thus won't add to the deficit, and thus remains eligible for "budget reconciliation" rules in the Senate and cannot be filibustered, requires making tradeoffs.
The whole point of the House Freedom Caucus is that they don't accept the concept of making tradeoffs. They want everything. No compromise. Not on anything. Not ever. That means they don't want revenue-neutral changes to tax policy. They want to change the tax code in a way that lowers rates. That would add to the deficit, make the bill ineligible for reconciliation rules in the Senate while guaranteeing Democratic opposition and a filibuster, and guaranteeing failure.
Tax reform is about making tradeoffs. The House Freedom Caucus won't let the party make tradeoffs. The last Chair of the House Ways & Means Committee, Dave Camp, tried to propose a tax reform package on his way out of town. They laughed at him. This won't happen.