As a teacher, first of all I would never write an email like this after a brief glance; I might consider writing a similar mail only after I fully correcting the test as the first one and a couple others, and even then I'd be hesitant to do so.

Worse, saying a student hasn't studied due to results is imo just a no-go. There are several possibilities beyond "not studying" for a bad grade (anxiety, misunderstanding questions (this can be students fault or the teacher's), the way questions are phrased, etc.). While ofc it can be an indicator of insufficient studying, if that's the case it's not our place to call it out; in the end only the student knows how much they studied. It's such a big blow to motivation when a student has studied hard and their teacher doesn't see the effort.