In designing concrete structures, normally maximum aggregate sizes are adopted with ranges from 10mm to 20mm. Does an increase of maximum aggregate size benefit the structures?

Basically, the force supplied by a concrete compression machine is a definite value. For normal concrete strength application, say below 50MPa, the stress produced by a 150mmx150mmx150mm cube is sufficient for the machine to crush the concrete sample.
However, if the designed concrete strength is 100MPa, under the same force (about 2,000kN) supplied by the machine, the stress under a 150mmx150mmx150mm cube is not sufficient to crush the concrete cube. Therefore, 100mmx100mmx100mm concrete cubes are used instead to increase the applied stress to crush the concrete cubes. For normal concrete strength, the cube size of 150mmx150mmx150mm is already sufficient for the crushing strength of the machine.