Interestingness helps but not the point
Startup conditions are chaotic and every new person takes management + training overhead. Internship applicants who have well-done and challenging projects have shown the energy, self-management, know-how, & self-learning to get projects done in mini-versions of these conditions. So every hour spent on them goes a lot further, and both sides benefit more.
Conversely, if someone can't get their projects done, the projects are too low quality for where it matters, or their skill are on too-different of a thing, at best, it's non-evidence. So you'll have to fall back to evaluating weaker signals like grades. At worst, lacking or failing at projects is a red flag that they'll struggle on the adult-sized projects as well.
For 'interestingness', probably more relevant is 'tied to the mission', but I think being youthful covers 80% of that for intern-level folks.
Failure to figure out fit may mean everyone loses. Interns are more about recruitment pipeline for companies, and I'm not sure that's the wisest way to solve that for a lot of startups if that's the goal. Likewise, startups not ready to invest in their interns (management overhead, training, etc.), or fail to screen for a good match in skills, can easily be a bad experience and opportunity cost for the students, who may have had a more pleasant, productive, and rewarding experience at a more mature company.