A gas turbine is a really bad idea for a car. They take a long time to get up to speed and spew a lot of hot exhaust in the meanwhile. There weren't practical cars at all.

I will argue that the finite nature of battery related materials, plus their weight, is a major impediment against all-battery powered cars in road transport. They are not "good enough" except as a stopgap until the next idea comes around. Which ironically could just be synthetic fuels, but more likely something like a hydrogen fuel cell car.

Fuel cells require catalysts like platinum which are far less common than anything in a battery.

They don't actually require platinum. Only types. And even then, it is basically the catalytic converter in terms of platinum needed. It is also 100% recyclable already.

All catalysts are way less common than the Iron, Phosphate and Lithium in a mass market car battery.

No, since sometimes it is also just iron or whatever. Not to mention that a catalyst is a surface, not a volume. You can get away with atom-thick layers of catalysts. Which is why even with platinum you only need a few grams of it. Cost of that is significantly less than a large mass of other materials.

Catalysts are consumables and need to be replaced regularly. Battery materials are recyclable.

Again no. Catalysts are endless recyclable.

Nickel iron oxide is the best catalyst for a type of fuel cell based on Anionic Exchange Membranes.

Cheap as dirt and you only need milligrams per kW. But it's so cheap you can use a tenth of a gram just to be on the safe side.