Why do you think petroleum cars can't switch back to using platinum? What benefits does palladium have as a catalyst? Price was once a reason, but that is no longer the case.
good question and I am not an automotive chemical engineer, so I don't want to lead you up the garden path.
this means a memory trip back to organic chemistry in my late adolesence...(don't read too much into that)
a basic issue for a converter is to remove environmentally harmful nitrogen (nitric and nitrous) oxides formed in the incomplete combustion of hydrocarbon fuels (air is 80% nitrogen).
Removal I think is done by removing or adding electrons between nitrogen and oxygen species (oxidation and reduction), so that in effect nitrogen is removed and what you get out the muffler is more carbon dioxide and water. Remember that these precious metals are excellent conductors of electrons, so it makes sense they would be used as an instrument of electron transfer. (note gold is also a good choice in catalytic converters).
In terms of this "redox", platinum is good at oxidation and palladium at reduction, so I would think that infers the different hydrocarbon mixes of refined petroleum and diesel lend themselves better to chemical reaction with relatively high ratio washcoats of palladium and platinum respectively. This may have to do with the relatively smaller number of hydrogen molecules attached to the carbons in petroleum distillate as those carbons have double or triple bonds (ie attached to other carbons rather than to hydrogen molecules). The ratio of carbon to hydrogen is therefore lower in petrol, due to these covalent bonds.
That's a lay take.
Rhodium, a byproduct of platinum, is the best of the bunch in terms of reactivity (ie binding) with nitrogen, but cost is insane and so is used relatively sparingly. It has the least elastic supply for reasons of there being no current mined primary ore bodies and due to current cost of extraction, a tiny worldwide supply. It therefore stands to be a better investment if investing in this group, I think.