I’ve also taken microbiology, and yes, the cultures in the dish are probably not what you need to be worried about. What you need to be worried about are all the other contaminated equipment and surfaces that you are going to come into contact with. I doubt an untrained child is going to know they have to sanitize everything with phenol every time they are finished, or that simply washing stuff in the sink is not going to sterilize it properly.
“Dang, where do I get toothpaste with Phenol?”
You don’t, because phenol is not fit for human consumption. However, your mouthwash contains alternate antiseptics that fulfill the same purpose. Failing that, you have your immune system to nip bacteria in the bud before they become problematic (assuming you are relatively young and healthy, otherwise the immune system becomes unreliable).