Board members are very useful in helping founders think big and hire executives. Board members are also a good forcing function to keep the company focused on execution. In my experience, companies without any outsiders on their boards often have less discipline around operational cadence. And board members stick with the company when things really go wrong, in a way that advisors usually don’t.
Board members certainly don’t have to be investors.
As a side note, bad board members are disastrous. You should check references thoroughly on someone before you let them join your board.
The companies that have had the biggest impact and created the most value have had excellent board members (and executives). I don’t believe this is a coincidence.
It’s a good idea to keep enough control so that investors can’t fire you (there are a lot of different ways to do this), but beyond that, it’s important to bring in other people and trust them to help you build the company.