I would like to clarify a few things.
Powder polishing only will bring the surface up to a glossier finish, but it won't remove moderate to severe etch marks. It will remove any light etch marks that are only dull and not something severe enough to be felt with your finger. The difference in the final polish depends mostly on the condition of the surface before you start. Why use a mechanical pad if the powder does this? Because mechanically refinishing first with smooth out the surface and make the powder polishing easier, and less time consuming, and give you a better finished product. Going through all the mechanical steps takes about the same time as it does to powder polish, so you're essentially doubling your time, and theoretically, doubling your money.
"chemical" polishing with a powder only uses chemicals during the actual polishing part, but leaves nothing on the surface. You are actually polishing the stone itself. There is nothing to wear off after.
for those of you wondering what the benefit of refinishing mechanically first vs. powder polishing only is; You get a better finished product, the surface is more resistant to light abrasion, and you make more money.
It all comes down to what your client is willing to spend and what you're comfortable doing.