Why do acids mix in water faster than bases?
You cannot compare the rate of first mixing acid with water with the rate of mixing the base with the diluted acid. You should compare the rate of mixing the acid with water with the rate of mixing the base with water instead.

The reason is that adding the base to the diluted acid will neutralize portions of the base during the mixing process resulting in lower concentration gradients that make the mixing slower.

A simple gedankenexperiment will show this. Consider a cylindrical tank with water of volume 1 with a mixing rod along the axis. Now put an amount of 1 acid into the tank along its axis. When the acid has made half the way to the wall of the tank the concentration in the inner volume is 4. The gradient is 4.

Now think of adding an amount of 1 base to the completely mixed diluted acid. When the base has made half the way to the wall of the tank, 1/4 of the base has already been neutralized. The concentration in the inner volume is 3. The gradient is only 3 compared to 4 before.