I do inspections on security in bowling and shows in my city, and they gave me as an excuse for the lack of differential circuit breaker the generation of harmonics and other elements as a trigger for differential switches. I asked some well-known electricians and some said yes if others did not know.
Not at all. Even if harmonics were problematic, IDs are called super immunized that are suitable for these environments. Do not accept an excuse of this type as there are components designed for this purpose. Even not all harmonics are problematic. I leave a couple of links for you to consult.
https://gesternova.com/los-armonicos-causas-consecuencia-y-soluciones/
https://www.sumidelec.com/blog/diferenciales-superimmunizados