"We" audit a sample of citizens and if any of them had large non-private transactions (for example, buying a house, or investing millions in a hedge fund) we demand they explain where the money came from. If they don't explain it, or explain it came from a transaction which they should have disclosed, we confiscate their property or imprison them.

It's hard to hide everything from the likes of the IRS.

> Do we bake in some kind of asymmetry like a sales tax where one party has a financial incentive to report the expense so we can check if the recipient declared it as income?

You essentially just described VAT.

Do we have something like this for income tax?

The distinction between income and consumption taxes is largely political. The buyer's consumption is the seller's income.

For example, VAT as applied to securities transactions is basically just another name for capital gains tax.

VAT isn't traditionally applied to the purchase of labor, but that doesn't make much difference because only expenses where VAT was collected on purchase should be deductible when it's collected on sale, so it just means the same tax is paid on the other side when the products of the labor are sold.