But not all payments you receive are income, and not all income is a payment you receive. See:
http://en.wikipedia.org/wiki/Haig%E2%80%93Simons_income.
Say I'm a shopkeeper. I sell you a candy bar for $2.00, and receive a payment for that amount? Is that my income? No. The credit card processing fee, the cost of getting the candy bar delivered from the wholesaler, and the cost of the candy bar itself must be paid out of that $2.00, but do not represent changes to my own wealth. Deductions exist to go from "gross income" (the payments you receive), and "taxable income" (the amount that your wealth actually increases).
Now, say I'm a farmer. I buy a new tractor. I should be able to deduct the cost of that tractor from what I make selling my crops. But should I get to take the deduction for the full value immediately? No! Unlike a candy bar, which is gone as soon as the customer purchases it, the tractor is a capital asset (an asset that is used to produce income). When I buy a tractor, my wealth just changes form: I have less cash, but I have a tractor. Over time, the value of the tractor will decrease. Eventually, the full cost of the tractor should be deductible, but because the tractor will help produce income over many years, the deductions should be taken over many years. Otherwise, because of the time value of money, the taxes paid will understate my actual increase in wealth. This is what "depreciation" is all about. Because it's impractical to actually sample the change in value of the tractor each year, it happens according to fixed "depreciation schedules." And when you sell the tractor, the difference between its market value and its value according to the depreciation schedule generates income or loss that must be accounted for.
Now, say I own a house (or stock). It's value goes up every year, which represents an increase in my wealth. Should I pay the IRS a tax each year based on an estimated amount? That would be very inconvenient, so we have a whole system of "realization events" that define when continuous changes in wealth must be "sampled" and tax paid.
As I noted in my post, a lot of this complexity just falls out of accounting. You're right that the various measures to use the tax code to create incentives/disincentives also complicates the situation, on top of the inherent complexity. But it's not a given that the value of these incentives/disincentives is less than the burden of the additional complexity.