"What is the harm in trying to identify the tiny, tiny percentage of children who are already experiencing gender dysphoria at a young age?"
The harm is
a) you are validating their misapprehension about themselves; agreeing that a child who thinks they are a pony, or a child of the other sex, or fat when they are thin, is harmful to them.
b) you are entrenching their misapprehension instead of allowing them to grow out of it as would be a normal trajectory
c) you are setting them on a path of alienation from their body, potentially harmful unnecessary medical treatment which renders them infertile and a lifetime of reliance on hormones and other unnecessary medication
d) you are homophobic; the majority of children who claim to be the opposite sex to the one they actually are and play with toys designated by our sexist culture for the opposite sex, grow up to be gay or lesbian people.
This is basically a bizarre, unethical way of "curing" homesexuality by changing future gay people's bodies to make them look like a different sex to what they are, instead of allowing them to be ordinary gay people in their own bodies.
That's harmful to the whole of society IMO but the most harmed of all, will be the children sacrificed to this insane fashion for pretending that biological sex means nothing.