or, Why are there so few polyatomic cations? What about the mechanics of an atom makes it so?
Welcome to PF;
The first three I thought of, off the top of my head, are all positive: CO+ , CH4+ , N2+ ... where do you get the idea that "almost all" molecular ions are negative? Is this something you have seen written down or an impression you have formed?
All of the ions that you listed are radial cations that are not very stable. The OP is talking about commonly encountered polyatomic ions found in ionic salts.
If you look at the list of common polyatomic anions (which is much larger than the list of common polyatomic cations), you'll see that many contain oxygen and are oxyanions. Perhaps the prevalence of these oxyanions is a consequence of life on Earth: Living organisms have made Earth's atmosphere rich in a relatively reactive substance, oxygen gas, that has reacted with many substances to produce the wide variety of oxyanions we see.
My understanding is that the OP asks why there are plenty of ions like CO32-, PO43-, MnO4- and so on, but only a few like VO2+ or UO22+.
I am not convinced presence of oxygen on Earth explains that - I have a feeling it is not that these are the oxyions we observe, rather these are "oxyions" that exist in general. And oxyions seem to be dominated by oxyanions, with a relatively low number of oxycations.
How many mono-, di-, tri-, tetra- (alkyl/alkenyl/aryl/etc.) ammonium/phosphonium compounds are there?
Tropylium, carbonium, diazonium, oxonium, sulfonium, pyridinium --- just a matter of digging around a bit, and the difference in populations may not vanish, but become a matter of which areas of chemistry one wishes to focus upon.
That's actually a great question! I don't know what it says about my education/studies, but it was never explained to me nor shown. I'm banking on simple observation...
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