I don't think Intuit has anything to do with why the tax code is complex. Their lobbying is for making filling out the forms complicated, such as by stopping the IRS from pre-filling forms with the information they already have.
The tax code complexity almost all stems from people not wanting to pay tax. That complicated the code in two ways. First, it means that we get exceptions and special cases written into the code either because people that want to pay less tax convince Congress to make a special case for them or Congress takes advantage of the desire to pay less tax to provide exceptions to motivate people to change behavior.
Second, it means that if there is any ambiguity or wiggle room in interpreting something, someone will exploit that to pay less tax than Congress intended them to pay. The tax code gets patches to fix that, usually resulting in an increase in complexity.
A great example of the later was that a long time ago a big company was going to give shareholders a dividend. This would be taxes as ordinary income to the shareholders.
Someone came up with an idea to turn that into capital gains instead. Rather than give a divident, the company first did a stock split, say 100 for 99. So each 99 shares each stockholder held became 100 shares. This is not a taxable event.
Then the company did a stock buyback, 1 out of every 100 shares. That decreased each stockholders holding by 1%, so every 100 shares a stockholder held became 99, and the stockholder got some cash. That is a taxable event, but it is capital gains.
Net result: every stockholder ended up with the exact same percentage of the company that they started with, with some cash from the company, and got to pay the lower capital gains tax on that cash instead of the higher income tax.
The tax code was patched to fix that. Buybacks became ordinary income. But it didn't end there. Consider a family owned business owned by four members of the same family. One of them is moving away and will not be participating in the business. The company wants to buy him out. It was generally agreed that this was not a buyback to dodge taxes--it is a legitimate buyback and should get capital gains treatment.
And so the patch to fix the buyback tax dodge needs an exception to try to recognize "legitimate" buybacks. It ends up having a formula that involves looking at the distribution of ownership before and after the buyback and having several criteria for recognizing when the distribution change signifies a legit buyback that should get capital gains treatment.
This was a fairly simple instance, so it only added maybe a few paragraphs to the tax code, plus some more to the regulations.
But that sort of thing is all over the code, sometimes just adding a few sentences, and sometimes pages.
Worse, when I moved to Chicago the state of Illinois wouldn’t even accept my taxes electronically because their form required one of a handful of authentication methods—the only one of which that ought to have worked for me was to use my Illinois driver’s license number—a 12 digit sequence; however, their form only permitted 8 digits. It was a significant hassle just to get them to take my money.
I’ve also had difficulties figuring out how much to withhold. In the US they give us a form that calculates “allotments” (or something—I forget the term) but it’s unclear whether more of those correspond to more or less withholdings and in any case the form computed incorrectly for me for several years (I’m sure it was user error somehow and senior engineers are just not reliably smart enough to figure it out, even with the help of HR) and I would end up owing thousands in taxes as well as a separate penalty for not withholding enough.
It’s maddening that our government makes it so difficult for earnest people to pay their taxes.