Ask HN: Should I leave and start my own thing?

I was recently hired as a junior IC in a small startup. After a few weeks there, I realized the company had no product and that the actual direction was completely different from what they'd sold during interviews. So far so good, it's a small company after all.

What is bothering me, however, is that the founders believe the current direction is a dead-end, and keep encouraging people to come up with new product ideas. They are not involved in the process, except for organizing meetings where they take notes when we tell them something that sounds promising. There is no team work, everyone is kind of left to their own devices. Half of the team is not doing any work, actually, and they seem completely demoralized. The only difference between working in this place and not working is the (below average) salary. My analysis of the situation is that the company is functioning like a startup incubator: founders had no idea what they were getting into and are asking employees to build a company for them, except we get no equity.

Now, during my stay here I've come up with an idea and spent my free time working on a prototype that looks promising. Sharing my idea with the founder feels wrong. Should I leave and go my own way?