So at what point do trans identifying men stop being just men and become TIM? When they buy a lipstick and a pair of tights? When they buy a bra and stuff it with socks, or do they have to have bra filling surgery? What if they don’t have surgery and their trans identity remains cosmetic, does that count? If it is just a question of “I am what I say I am” why can’t we say no, actually you are still genetically a man, dress how you want, call yourself what you want but you really can’t go against the binary sexual arrangements that every other mammalian species and most other plant and animal species use on our planet just because you have a feeling which is more likely to either be a manifestation of your latent homosexuality or a product of some form of dysmorphic mental illness such as for example we readily accept is the case for anorexia. We really cannot have a society where to mollify a tiny proportion of disordered men other men, with adverse intentions, are as a by product of “kindness” given free access to vulnerable women and girls.
And btw people aren’t “assigned” a sex at birth, sex is observed using the very useful physical clues nature has provided. Sometimes, if there has been some sort of chromosomal glitch, and the child is unfortunate enough to be born in a country where medical provision is limited , and additionally the social stigma of a child felt to have a physical anomaly is very oppressive, a decision might be made which later proves to have been unwise, Caster Semanya and the Algerian boxer are unfortunate examples. But these are rare, and do not actually affect a human beings chromosomal identity of being male or female.
DNA testing in youth and most amateur sport should as you say be unnecessary, especially since once again there are usually sufficient physical markers which identify sex - especially in males post puberty - and which should be enough to make it clear whether an athlete should be competing in open or sexed classes. When it does become necessary, and should be obligatory, is when those very clear physical markers are ignored or deliberately fudged in order to obtain advantage in professional sport. This could be sorted by making a simple, universally accepted mouth swab test being obligatory for all professional athletes and sportspeople.