A lot of life involves reasoning: taking this information you have and making hypotheses that connect different pieces in a way that provides a deeper understanding of them.

The more information you have muscle memory for, the more you can use to reason about. This is why having more knowledge generally helps you to tackle more complex problems.

If you have memorized knowledge you have also pre-processed it in a way that aligns with how you think, thus helping you during your reasoning. 

The problem with not memorizing is that you're limited by the lack of data points, or nodes that you can make connections between. In short, you're limited by your lack of understanding of what to look up.

A common example is that many engineers due to their overuse of StackOverflow end up solving problems without actually understanding how they solved them, or even worst, without learning anything. After a few months, if the problem arises again, they would try to brute force searches on Google to find again a solution.

Memorizing information gives you a concrete organizational scaffolding and context in which to put new information. Memorizing an organized set of facts means that new information can be inserted in an orderly way, sandwiched, or enhancing other facts in an organized framework.