I know that floor poly is not the same, but why wouldn't this polishing issue work the same way.
I think the difference is that you're talking about a homogeneous material, gloss polyurethane on furniture I think it was.
If the material itself is homogeneous (or uniform throughout) then I'm sure polishing would work. After all, they polish Carnauba wax and acrylic floor finishes to make them smooth (and therefore glossy). They polish gem stones, ordinary stones and metals to make them smooth and glossy, too. But, these are all homogeneous materials.
The difference here is that the floor finish isn't homogeneous. It has tiny particles of (prolly) sand embedded in it to make it dry to a rougher surface than it otherwise would. That sand is harder than the floor finish, and so I can't see how it's possible to polish such a surface without the polyurethane being worn away faster than the sand, and thereby always leaving you with a rough surface.
That is, I can't see how it's possible to polish that floor finish to wear down the hard sand particles more aggressively and the softer polyurethane less aggressively to ultimately achieve a flatter smoother surface than you started with.
Also, even if this was a homogeneous material, like a gloss polyurethane, it would still be necessary to use a very powerful machine to polish the floor finish to make it smoother. My understanding is that waterborne polyurethanes are close to the same hardness as oil based polyurethanes, and I've never heard of anyone polishing oil based polyurethanes to bring out the gloss the way floor wax was polished 60 years ago. I presume that's because of the nature of the machinery needed to do the same job on a the much harder floor finishes being used nowadays.
I'm not saying I'm right and DangerMouse is wrong, or vice versa. I'm just saying that when I think about the process of polishing a satin poly floor, I find myself confronting problems that convince me that it wouldn't work. And, so, I have an obligation to bring my reservations to the attention of the poster. I'd be wrong in not speaking up. Someone else might post and explain why my thinking is wrong, and I'd hope they do. We would all benefit from reasoning that we all agreed with that leads to a unanimous opinion on the matter.
Anyhow, it's precisely these kinds of technical discussions that should be the life blood of DIY forums. Too often, however, they turn personal and degenerate into insult hurling contests which makes everyone look like a fool. I'm glad we've been able to keep this discussion on a technical level.