So there are a few factors at play. One key thing to remember is that a doubling of palladium prices (even from current levels) only adds about $200 to the cost of the car, so the incentive to switch isn't as massive as it's made out to be (but the incentive is there, it's just a matter of time in my opinion).
Another key consideration is that catalytic converters and emission treatment systems are a lot more complex than they were in the past, and have been optimised for Pd use (so without a lot of R&D, you're not going to get similar levels of performance with a 1:1 platinum-palladium switch). The R&D spend is going to be significant, it's my view that automakers don't want to be the sucker who switches first and helps balance the market for their competitors - also if everyone independently switched we'd be in a position where the platinum market would be in a major deficit (not as big of a deal, however, as there are plentiful above-ground stocks). Also, carmakers R&D budgets are tied up in electric vehicle research - with petrol and diesel vehicles futures very uncertain beyond the medium term.
Further hampering a switch is that carmakers risk having to perform super expensive recalls if the longevity of these platinum catalysts turns out to be sub-par.
But I do think that the switch will occur soon at some level (likely by reducing already-low palladium loadings in diesel cars, and substituting small volumes of palladium in larger-engined petrol cars - where the engine runs cooler and the longevity of the catalytic converter's performance is less in question. Especially when above-ground vaulted supply starts to dry up.
Final point: It's not really possible to replace rhodium economically (even at current ridiculous prices) with platinum or palladium. Pt and pd are oxidation catalysts, whereas rhodium is a super efficient reduction catalyst - this makes it super effective at reducing NOx emissions (though there is some substitution pressure from ammonia-based emission treatment systems that are effective at reducing NOx).
PS: These are just the basics - I've glossed over a lot of points; but I wouldn't have a job if I told you everything
