First, I'd dispute your claim that majority of Badminton pros could go pro in other sports. Definitely some of them, being fast with good hand-eye coordination is going to get you places. But there's a limit.
If you can make it in NFL, NBA, MLB, etc, you do. And the true superstars often have the option of multiple sports. Patrick Mahomes was drafted for both the NFL and MLB. Lebron James got tryouts with a couple of teams. Bo Jackson had a professional football career and a professional baseball career concurrently.
Football, baseball, rugby, soccer, and basketball all "poach" from the others' sports because athletes gonna athlete.
But badminton is already a cousin to tennis. And if you can do well in tennis, you should do that. The only reason to be the best in badminton rather than the best in tennis is some weird obsession. You choose niches when you can't or don't want to compete in the general arena.
Second. It's not a choice between eSports and traditional sports.
It's a choice between eSports and almost anything else. The goal isn't to play something with sports in the title, the goal is to earn a living. And the best eSports player in the world is getting outearned by mid-level accountants. You could go to college for four years, spend under $40k, get an accounting degree, then go get a job at any accounting firm or in-house at any company, and be earning about $60k a year.
And if college isn't for you, you can become an electrician's apprentice. Earn about $40k a year while you learn how to be a fully licensed electrician. Then after 4 years, you get licensed and can double your money.
Ideally, you should choose the thing that can provide you a decent living while leveraging your skills and/or talents without overworking you.
But eSports doesn't provide a decent living on average. And it overworks everyone.
And that kind of ignores that ability and/or skill is only part of it. The people who are currently the best in areas where the money isn't there are only the best of the people who can be bothered to do it. The hypothetical best CounterStrike player possible probably does not even play the game. Because somewhere, early in the sieve, they did the math and realized the effort required to maintain their position was not worth the reward for doing so. And it could have been when they were the best Quake deathmatcher on their dorm floor. They realized they could continue playing or study for midterms. And they chose their midterms because that was going to secure the bag.