Surprised to realise I've had my PC (except GPU) and FHD monitor since 2011. The days of everything doubling in performance/capacity/pixels every 2 years or so are long gone.
It might be possible to get that to do the rescaling from 1080 to 4k. Could result in better image quality, depending on how good the monitor's scaling hardware is.
yeah that's what I do, my GPU isn't capable of playing most games at a decent frame rate at 4k so I set them to 1080.