Proper means fully removing the harmonics of the square wave. Take a 44.1khz input single, apply 8x OS, and then sufficient LPF to get the response down by 384khz, where the first image appears. You will get the same output as the original, in that 20-22.5khz 0-96dB range. Outside of this sure, high rez is unquestionably superior.
Oh, and dont think you can get away without a reconstruction filter on high rez either.