Yes, antibiotic resistance is a concern if you start handing out antibiotics like candy, but if PANDAS is truly as rare as everyone would have you believe, then prescribing antibiotics to every kid that comes in with a PANDAS profile is not going to move the needle much with regard to global antibiotic resistance.
Alternatives:
Prescribe them anti-psychotics or some other medication to sedate them?
Likely much higher side-effects and risk profiles than antibiotics.
Send them to a therapist in hopes that the therapist can behaviorally condition that aggression away?
Bad news: talk-therapy for aggressive behavior in children has terrible outcomes. Most likely scenario in the mental health system is that they end up in an intensive group treatment setting somewhere with other aggressive children, learn more sophisticated aggressive behaviors, and gradually get worse.
On the other hand, antibiotics have a fairly low risk profile. Some pediatricians do literally hand them out like candy when kids come in with an ear infection or sore throat. Maybe stop prescribing antibiotics for those kids, tell them to try some tea tree oil or some other natural remedy, and save the antibiotics for the kids who fit a PANDAS profile instead?
The idea of PANDAS from occult (aka hidden, not producing positive test results) strep infections is less proven and considered rare, although it is mentioned in official treatment recommendations such as those above.
The problem providers face is that some parents will read about PANDAS on the internet and assume it is the explanation for their child's problems, despite having negative throat culture. They jump from doctor to doctor demanding antibiotic treatment despite the negative test results, guided largely by their internet research. It's not hard to find PANDAS parent groups on Facebook or Reddit where someone can post vague symptoms and a chorus of group members will response "sounds like PANDAS".
The difficult part is that for some of these patients, PANDAS might be the right diagnosis. However, once a diagnosis becomes a cult favorite on the internet doctors get inundated with parents demanding antibiotics because their Facebook groups told them that's what their child needs.