Even though I largely agree with your conclusion, I strongly disagree that this problem is made artificially difficult.
The fallout of a decision like this for professional athletes who are trans is huge. That fallout and the effects from that decision should not at all be taken lightly.
Having an MTF proffesional athlete to compete in the male category is going to probably cause a lot of disphoria. It will also make it much harder from them to be accepted as female. Many people will question "If she is a woman, why is she competing in the male category". Hence it would probably cause many MTF professional athletes to simply decide to drop their profession.
Transitioning is already hard. Adding "drop your profession" to that makes it that much harder. Especially to professional athletes to whom "being an athlete" is probably rather important. Just dismissing these concerns as "easy" is wrong. The impact this will have is huge and deserves significant consideration.
I believe that, on balance, even when considering the above, there are still cases where MTF athletes should be barred from "women's leagues". At least in sports where their biology gives MTF athletes a significant advantage. But that is a close and difficult call to me. Not at all an easy one.