> This would imply that education degrees make their recipients better educators.
Not necessarily. It might just be an artifact of mandatory certifications. Suppose that teacher training were completely useless (debatable), but nevertheless legally required (mostly true, esp. for public schools) and expensive in terms of time or money (definitely true). I think you’d still expect increased earnings in those who obtained the certification, if only because they are now eligible for jobs where the supply of potential employees is limited. If they leave the industry, however, that certification often counts for very little, and the pay bump disappears. None of this, of course, tells you anything about conditions across industries.
The quotes in your comment are missing some important context. As §2.1 of the linked paper says, nearly all teachers in the US are somehow licensed, but this can be part of an education degree or an “alternative certification” for those with other degrees. Those two types of training are what the paper compares, not trained vs totally untrained. Critically, both take time and money.
The advanced degree data is also hard to interpret. It could be that a masters is totally worthless. However, selection effects also seem possible: teachers with more training could be given more challenging students or courses, or, as the paper proposes, underperforming teachers could preferentially do a masters to shore up their skills. They could also have more out-of-classroom responsibilities (e.g., curriculum development or admin), which would be consistent with how advanced degrees work in many other fields.
Anyway, all this is to say that “haha teachers are overpaid dummies” is, IMO, too simplistic and not supported by the data either.