However, "The state already requires commercial carriers to provide the therapy, also called ABA, to Floridians with private insurance" if the therapy is questionable in its effectiveness, why are private insurers required to provide it?
Because the therapists who provide the therapy organized themselves and their patients/customers to lobby the legislature to pass the mandate, while most people simply weren't paying attention. This is why all sorts of treatments with relatively few providers and users are mandated by state governments. Each one doesn't seem like much, but all together, they add up to much higher insurance premiums for everyone.