then again, if the mom sent her kid to such a dangerously unqualified school, she may not be the most well informed person

It's not even small claims court; the producers pay the settlement if one is awarded. Judge Judy is a game show where people can be publicly shamed or make a small amount of money. Usually both, but no one has ever lost money from being on Judge Judy.

In answer to your question, she's on the show because people without credentials who run religious schools aren't sleeping on piles of money, and people who send their kids to those schools tend not to have lawyers on retainer. This was her only shot at getting paid.

suing the school out of existence would be the best possible outcome here.

There's no school to sue out of existence. It's just two idiots and the closet they lock children in. This is America, they can rebrand and start over at any time.