Speaking for myself, and remember I'm an improviser rather than a classical player, I tend to favour actually feeling two or more independent things, not necessarily notatable, going on simultaneously. At first it seems much more difficult than using special tricks for special cases, counting and so on, but once the ability is cultivated, it is applicable anywhere. I certainly cannot think those things out; if I did that I probably couldn't start. Rhythm in general is very much an almost physically perceived phenomenon for me.
Cases like Fantasie Impromptu, and similar instances of two very regular streams, often rapid, with different cycles, seem to me hardly polyrhythms at all. Unless they are played slowly, the ear doesn't perceive enough landmark notes to make things difficult. If the rhythmic streams are not regular, but have internal phrases within them, then that is very much more difficult and nothing but truly playing and feeling two things at once really works. Very simple examples of this latter occur in the Rhapsody In Blue.
Of course many jazz players acquire the intuitive knack of playing many things simultaneously but as attempts to write it out are seldom made the process is not considered "polyrhythmic" in any special sense, although it is - very much so.
It is always a delicious surprise when, listening to my improvisations, I realise three or four very clear, rhythmically independent ideas are going on simultaneously. I haven't the slightest idea how I do that. It certainly isn't deliberate and I think I would do well to desist from trying to produce it at the conscious level. Nonetheless it's there, clear as a bell.
As you will have gathered, I am utterly obsessed with rhythm. I think it is the soul of music.