No, it's not. Yes, on average men are bigger and stronger than women, but that's just an average. It's no more "irresponsible and dangerous" than letting Zdeno Chara play against Johnny Gaudreau. That size difference is much bigger than the average size difference of biological men and women.
No, it's not conceivable that that could happen, not at this pace. There are still vanishingly few transgender athletes, and even fewer of them are in any way dominant.
"Sounds like" and "Usually pretty obvious" are terrible measurements. Obviously you're not going to notice the non-obvious cases, and just in general you can't start checking people's genitals on wishywashy ideas like this.
First of all, "obvious cases of biological men" needing to be "rooted out" is not a thing to begin with, and second, a genital check does not help. Here's an example of someone who would be categorized as a woman based on a genital check, Buck Angel.
As long as people are not competing with genitals, there's no point in checking the genitals.