The CPU is just as important here, because we're talking about 240 fps. This is EXTREMELY CPU heavy, and no CPU right now is fast enough to deliver 240 fps in every single Game, even in the lowest possible Settings.
Let's say you go down to 720p Ultra, the CPU still needs to calculate and deliver 240 fps.
It doesn't matter anything, if it's 720p, 4k, or even 16k.
If the Target is 240 fps, the CPU Load is exactly the Same (unless there are other factors like object distance etc)
You say CPU Load gets lower with higher resolutions only comes from the Fact, that the same GPU will produce LESS FPS in higher resolutions/settings, which means the CPU has to "deliver" less fps --> Less work for CPU.
CPU and GPU are independant in their Work. And just, because Resolution is higher, it doesn't mean, that the CPU magically has less work to do.