If you can’t break down something, memorizing the answer only teaches you the answer to those problems. Each piece of mathematics is a building block that can be used to help understand another part. You are skipping past the part of why 2+2=4 because it seems forthright and immutable. But, memorizing that means that there may come a time when 2+2 isn’t equal to 4, and without the knowledge of how to get there, could you then solve for 2*3?
This seems silly (and maybe a little abstract), but it’s meant more as an example to show why knowing how to break things down could solve bigger problems later on. Learning multiple ways to solve a problem can be really helpful!
It’s really just meant to show that it can be broken down, not that it is faster (because it isn’t).