Consoles are more and more supporting VRR, as are televisions.

But yes, given the limitations of the hardware, they often offer two modes - a high framerate but lower quality mode and a high quality but lower framerate mode.

>I often see people targeting frame rates way beyond their display’s refresh rate. I’m not sure whether this actually provides a real benefit or whether they’re chasing a placebo effect.

Pixel refresh is only one part of latency. A higher framerate will lower several other parts of the overall latency. Monitors Unboxed has charts that visualize the amount of latency for each step.