The issue is that all the problems I really care about solving are not “products” in the sense that they’re not commercializable and no one cares about them but me.
Dude just go for it. Even if it isn’t a product and cannot be sold, having a project that demonstrates your skill is worth more to the right recruiting staff. Also, in trying to solve a problem you care about, you will find challenges and the right motivation to learn the tools to overcome them.
