Marble is calcium carbonate. Rainwater is mildly acidic, and water that has run over stone, planting or paving is often more so. Acid dissolves calcium carbonate — slowly, but continuously and unevenly, because flow rates across a carved surface are never uniform.
On a honed surface that etching is invisible: the finish is already matt, so a marginally more matt patch reads as nothing at all. On a polished surface it is glaringly visible, because the polish is a specular finish and etching destroys specularity locally. Within two seasons a polished fountain bowl has bright areas where water does not sit and dull areas where it runs, and the boundary between them is a hard line.
It cannot be fixed on site. Re-polishing a carved surface in situ is not realistic, and even if it were, the same pattern would return. So the decision has to be made before the stone is finished, which is why we hone anything that will run wet as a matter of policy rather than preference.
The same logic applies to horizontal exterior surfaces generally. A polished plinth top will etch from standing rainwater; a honed one will not show it. The one place polish genuinely earns its place outdoors is inscription, where the contrast between a polished ground and a cut letter face is what keeps lettering legible for decades.
If a client wants the look of polished marble in a water feature, the honest answer is that they want it for one summer. We would rather explain that than deliver it.

