If you correctly infer the _structure_ of the problem, then you're going to have an easy time solving it. If not, you'll use a great lot of time hunting for a fruitful angle of attack.
75% of interview questions can be solved with some form of BFS/DFS and they’re largely a hazing ritual these days. I’m saying this as someone who recently got offers from 4 of the big 5 companies
Then once the same intuitive leap has been used to solve many different problems, and gets taught in school, it becomes a “simple trick”, or even just a “standard technique”.
If this same method is useful for solving a wide range of structurally similar problems, it will go through that process, and eventually become thought of as a “simple trick”. If it is only used as a one-off for this particular proof, it will remain one man’s genius idea.
I've heard students complain that graduate qualifying exams are a form of hazing for people hoping to become pure mathematicians, and although I don't entirely agree with that sentiment, they do play a similar role in weeding out people based on preparation rather than ability to generate deep, novel insights.