Usually you won't flood fill an entire layer with power on just 2-layer PCB but if you have very little routing why not. A power distribution board that just connects a few connectors (and maybe a few bulk capacitors) together but has little other circuitry would be a typical example where I have done a 2-layer design where one layer is ground fill and another power fill. This can be also called a "DC link sandwich", there is not that much coupling capacitance but that's not the point, the lack of inductance (and easy mounting of capacitors) is.
Typical and good way of using pours/fills for power is to draw the polygon over some limited area and let the EDA tool handle all those tiny details that take a long time to manually draw, but still not waste the whole layer.
"Confusion" is a strange argument against it, given how usual power planes and relatively large power fills are (for obvious reasons). If you just assume any large copper area is ground, you are assuming wrong. OTOH, if you are carrying some hundreds of mA between devices that have proper bypass caps in them, a full powerplane can be called overkill, a simple wider track would work the same.