That's absolutely not the case. They lobby to prevent the IRS making their own version of TurboTax, not lobbying to make the tax code more complex. Taxes are complex because we have little real oversight but a lot of deductions and credits. The IRS literally cannot track everything they offer deductions for, so it goes largely on the honor system until something seems fishy.
If you have a house, you have deductions. If you added solar to your house, you have deductions. If you bought an electric car or a hybrid, you had deductions for a while there. If you rent you have deductions in some states. You have to list your dependents for credits.
The IRS is incapable of tracking all of this.