You misunderstand the interaction of sharpening and polishing. To some extent they are separate processes, but by and large they are part of the same process. We sometimes use the terms as though their action on the knife were completely different things. I know I do; and if that's part of your confusion, I apologize.
The abrasives embedded in the stone have a given size. When the knife is rubbed on the stone, the abrasives scratch the side of the knife, continuing all the way up to the edge. The resulting scratch size depends on the size of the abrasive. At the very edge of the knife, the scratches create teeth.
Thus, the size of the teeth are determined by the size of the scratch which itself is a product of the size of the abrasive. This is true, even if the edge is created by deburring.
However -- and here's where you confusion seems to set in -- this is true for every grit size along the polishing ladder.
When a finer stone is used to polish the knife after a coarser stone was used to sharpen, we use the term "polish" as a way of saying that the finer stone will reduce the size of the coarse stone's scratches. If the edge is polished out as far as the stone will take it, a new burr forms. When the knife is deburred, a new edge is created. And the size of the teeth on the new edge are determined by the size of the scratch left by the finer stone.
Everything else being equal (and it isn't) it will take more works for a 6K surface to bring a 1K bevel to 6K than it will take a 2K surface to bring a 1K bevel to 2K.
But remember: (1) A 2K bevel is not a 6K bevel -- the comparison is apples to oranges; and (2) Some 2K stones are very slow for 2K and some 6K stones are very fast for 6K, so it's not possible to make specific predictions without naming the specific stones.
Some people like to work with relatively small tight jumps between grits. Others prefer larger. I find, that for most people, the best strategy is to use the fewest number of strokes through the entire process. 1K to 6K is a fairly large jump, but is quite doable with many stones. If it weren't, 1K/6K combination stones -- like the ubiquitous King -- wouldn't be nearly as popular as they are.
I find that using a coarse stone, a 500# for instance, for ordinary sharpening -- when the knife doesn't need repair, thinning or other profiling, is counter productive and inefficient. It is counter productive because a 500# stone not only removes so much metal to create a burr, but requires that a great deal more be removed to polish out the 500# scratch. It is inefficient, because polishing out the 500# scratch with a 1K - 2K range stone, and pulling a new burr, requires as long as it would take to use the medium/coarse stone to begin with.
Remember, that the process of creating a burr and deburring is NECESSARY, because that's the process by which the edge is created.
Remember also, there's no single best combination of stones for everyone.
As a general rule: A good 1K stone is an adequate lead in for a good 6K stone. But if your using a 1K as a rung of a grit ladder which goes finer than 6K, you would probably be best served with an intermediate stone of some type.
My water stone kit goes to 8K. I usually start sharpening on a Bester 1.2K, then use a 3K Chocera to bridge the gap to the Gesshin 8K. Even though my 8K is very fast for an 8K, it still saves strokes to use the 3K. 1.2K to 3K isn't a more optimal jump than 1.2K to (say) 5K. Rather, I like the 3K Chocera edge as a final edge for those knives I don't take to 8K, but don't like a 5K edge for any of them.
It's helpful to think of stones in terms of their function within a comprehensive set, and at a very general description which balances function against a range of grit sizes rather than at particular grit numbers. This viewpoint helps to reinforce the idea that particular grit numbers can be misleading and are typically overemphasized.
A generalized kit like mine could be described as:
- Coarse stone, for profile and repair
- Medium/coarse, to pull the first burr;
- Medium/fine - Fine, to pull the second burr and create a refined -- but not necessarily final -- edge; and
- Extra fine - Ultra fine, to create a very refined, and final edge.
FWIW, my water stone kit, in particular, goes:
- Beston 500, coarse;
- Bester 1.2K, medium/coarse;
- Chocera 3K, medium/fine;
- Gesshin 8K, extra fine.
Let me tell you about the reasoning behind the kit, so you can get an idea of how much happenstance can sometimes be involved.
My old water stone kit was stolen, a long with my Japanese knives. My oil stone kit was more than adequate for my Euro knives so I wasn't in any particular hurry to replace the water stones, but you know how that goes. The no particular hurry period didn't last long. In a sane fashion, I decided on a Bester 1.2K as the "key" stone; and also decided on a Beston 500, a Naniwa SS 3K and a Naniwa Pure White 8K.
A friend of mine, who tried every stone on the market as they came up, wanted to get rid of his Beston, Bester and Naniwa SS 8K. Since the SS 8K was essentially free, I figured wotthehell, might as well try it. I mentioned, online, that I was going to fill in the kit with a Naniwa SS 3K, and another friend offered me a brand new Chocera 3K at a price far too good to refuse. The SS 8K eventually died, and I replace it with the Gesshin because the Gesshin is the best 8K on the market. I still think the Pure White is better value, but I tried the Gesshin at the JKI brick and mortar, was extremely impressed, could afford it, so wotthehell.
I could replace the Beston, Bester and Chocera with a Gesshin 400 and 2K, and -- because the Gesshins are so fast and have so much reach -- end up with as versatile and complete a set, but the kit works perfectly well as is... so there's no particular hurry. If you think I'm saying that, as a rule, a 2K can replace a 1K and 3K, you're still mired in numbers which seem to mean more than they actually do.
But if you think that "no particular hurry" may be replaced by "wotthehell" at any time and without prior notice, you're starting to grasp the process.
Hope this helps,