Correct me if I am wrong, but I don’t think there is any specific quals needed for this? Or Something akin to a rating in order to teach the theory?
To be able to offer these courses you need to be an ATO (Old RF) - complete with a "Head of Training" and a "Chief Theoretical Knowledge Instructor" (These may be the same person, and may not necessarily be known as those post holders). It takes some work to obtain an ATO to undertake this type of training.
To be able to teach on this or any ground school you have to satisfy the CTKI/HT that you have the required knowledge yourself. Some CTKI's may require more in the way of satisfaction than others but you don't have to have a FI Certificate or an AOPA Ground Instructor Certificate (if they still exist)
These courses are not meant to be the whole teach - the student is supposed to have at least read the books before attending. In much the same way as there are brush ups for CPL/ATPL lessons these PPL courses exist and provide, IMHO, a valuable service. I agree, some students don't do the pre-study and some courses are a little 'light on content' but that doesn't mean they all are.