It sounds like a bigger impact would be removing idle load on laptops

Chrome for example in a recent update touted improvements to battery life by reducing the scheduling of work on background tabs. Windows Battery Saver mode reduces the scheduling of background processes, delays houseeeping like indexing, and nicely asks applications to not perform bulk background operations (e.g. OneDrive syncing).

Parasitic load is never going to be 0 ... even if you have an operating system running just two processes that both immediately yield their time the second they get it, the OS has to wake the CPU so it can schedule their altruistic behaviour ;-)

The question is how much power do you draw when running these teeny tiny background things? When you're running on a BIG.little modern mobile processor like the A13, very very little. When you're running on a big ol' full-fat x86, even if you wake the beast for something tiny, it ends up being expensive in aggregate.

How does the computing load of an idle laptop compare to a phone going full-out on a benchmark?

I don't know what you mean. When I talk about parasitic load, it's not a serious workload. Timers ticking, UI drawing, maybe a few bytes on the network here and there. Just idle stuff. Running SPECint is balls to the walls, relatively speaking.

Mobile SoCs are incredibly efficient. They've been designed from day 1 to optimize for idle power draw to support long standby times.