I don't think the secret is usually the idea. The secret is usually a method of execution that lets you get to the finish line, where everyone else was too slow and ran out of runway.
Which is to say, if you're the right person at the right time, you don't know the secret; you are the secret. Your skillset (or your team's skillset) is the secret.
The tech that just became possible to leverage that nobody else has noticed yet but you're familiar with from its prototype days is the secret. Being able to bring your experience solving problems with 40-year-old systems to analogous problems in modern spaces is the secret. The pitch is not the secret.
As you say, the secret likely is not often the idea per se, as truly original ideas (i.e. potential Nobel prize-worthy ideas) are truly rare, and often difficult to recognize as such. They are much more rare than successful startups.
So, banking on an idea alone as the route to money is not usually as smart move, unless... the idea is really innovative.
My own take is that truly great ideas are as rare as hen's teeth, i.e.those that fulfill your description.