So, I think the point you’re missing is that how results are proved is just as important as the existence of a proof (in fact, I’d say it’s often more important

So, I think the point you’re missing is that how results are proved is just as important as the existence of a proof (in fact, I’d say it’s often more important). That’s why people are often excited about new proofs of old theorems, and why the Simon’s foundation chose certain problems to be “Millennium Problems” - the techniques developed to solve the problem would, ideally, drive progress in that area of mathematics. The Poincaré conjecture is interesting because it was a simple statement that ended up being very hard to prove. How someone proved it, and understanding why such an innocuous statement is so difficult to prove, is far more interesting than knowing that the obviously-true-sounding statement is true.