The number of speeds of the rear wheel and the size of the chain wheels have nothing to do with how fast a person can ride. It is the rider that decides. It has to do with mechanical advantage. Sure, a 52/11 is faster than a 48/13 in theory, but if I can't spin the cranks at the same cadence, then I won't be going faster. I will go about the same speed in reality.

I am only so strong and can't get any stronger because of mechanical advantage. I can only turn the rear wheel at x amount of revolutions. Whether this is done with a 52/11 or a 48/11. But, as mentioned above, if I try to use too high or too low of a gear ratio, I will tire more quickly and not go as fast over a longer distance. Sure, I can use the 52/11 to pedal and only have a small cadence, but I will tire my legs quickly and not be able to keep the speed up. But if I find a gear ratio where I can get the proper cadence for me, I can pedal at the speed for hours. The same is true for a gear ratio that is small.

If you are trying to get more speed, don't change the crankset or the cassette, change the rider. You need to train harder and properly. Unless you are constantly using the big/small already, then you do need a better gear ratio.