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The rule applies to new cars, fuel will still be sold after 2035. Of course, at some point gas stations will begin to close and the price will begin to rise, so there will be more incentive to buy a new car. Weigh that against the fact that EV fuel is much cheaper per mile than gas, EVs require less maintenance and that by 2035 will be cheaper upfront than a similar ICE car.

Sorry, but I don't understand why fuel price should rise if the demand takes a dip

The EU carbon price will continue to go up. Fuel will get hit with it when crude oil crosses the border and during refining.

You do raise a good point about the size of that effect vs that of lessening demand.

State(Superstate?) market intervention

The rules seem to target new cars not old.

Why would they be useless ? You can use them until they die.

The mandatory vehicle inspections [0] will likely cut them down before they die a "natural death".

Links:

[0]: https://en.wikipedia.org/wiki/Vehicle_inspection

This only affects new cars.