Wouldn’t this, in the end, make cars have to shift to a lower gear, thus keeping about the same RPM, and thus eating about the same amount of fuel

That’s not how cars work, they definitely don’t use the same fuel in different gears at the same RPM. See this Wikipedia article for a discussion of speed vs fuel economy.

And as pointed out by the the FAQ, that’s doesn’t not factor in acceleration:

Will driving at 20mph mean I use more fuel?

No. Fuel consumption is mainly influenced by the way we drive – driving at a consistent speed is better than stopping and starting. Accelerating up to 30mph can take twice as much energy as speeding up to 20mph.

A default 20 mph limit and a smooth driving style, can help avoid unnecessary speeding up and slowing down, saving fuel.