What is a higher population actually good for?

You don't need to always have maximum population. But it is needed to maximise your money earning. You can tap on the money icon on the top right and check the 'efficiency' rating. if it is below 100% then you don't have enough population to make use of the bank level you have to maximise your income.

There will also be points as you upgrade your base that you need to reach a certain population level to continue.