I was expecting that fast clicking the Left mouse button (attack) would be faster than simply holding the mouse button down.

For example, using a mob grinder, I would usually be able to fast click the mouse and make more hits per second, as opposed to holding it (on pc java version)

However on MCPE it doesn't matter whether I hold the Left mouse button or press it quickly, it still hits at the same rate, roughly once per second. (same if I hold or rapidly press X on keyboard)

Using the Right mouse button works correctly. It allows you to place blocks or use bonemeal as fast as you possibly can.