The landscaper already has to pay 15.3% off the top in self-employment taxes (payroll taxes). He then has to pay his regular federal income taxes. Let's say he's in the medium backet: 25%. So that' puts his tax rate at 40.3%.
Let's try you story using current tax rates.
When a landscaper faces a 40.3% income tax on the money paid to him or her to mow a lawn, won't they (and the homeowner) be tempted to just exchange some cash and avoid the 40.3% by having the landscaper charging 20% less to the do job, and thus avoiding another 20.3% in taxes?
Last I checked, 40.3% was a lot more than 19%, and is a lot bigger incentive for people to cheat the system by working cash deals under the table.
Your hypothetical ignores that the 25% rate applies only to the excess over $76,900 (assuming the landscaper is married), the landscaper pays only $9,500 on the first $76,900 (assuming he takes no deductions, even the ones he is entitled to). So the rate for the first %76,900 is more like 12%, again with no deductions. In the real world the rate is more like 5% after the typical deductions.
The combined FICA, Medicare, and income tax for the landscaper today are not much above the 18%, and yet people still have a tendency to avoid the taxes. So there is nothing to suggest that having a sales tax and an income tax will reduce the size of the IRS, or the amount of enforcement they have to do.