I am of the generation to have friends called Karen and I really feel for you. I don't know how that name got associated with the stereotype - none of the Karen's I know are like that. It reminds me of when the name Nigel became associated with the phrase "Nigel no-mates" when I was a teenager and I had a friend called Nigel who hated it. As a parent it was one of my fears that the name I chose for my child would become stigmatized like that as some stage later in their life but unfortunately is just another thing parents have no control over!
My daughter (year 5) got one of those letters from her class teacher and she was really cynical about it. The tone did not match how her teacher would usually communicate and at 10 years old my daughter already knew that the sentiments were not sincere. Kids are smarter than we give them credit for! One of the other teachers at the school gave them each an novelty eraser to use in the test and a note with a matching comment (e.g. my daughter got a cupcake eraser with a note saying "NAPLAN is a piece of cake" and her friend got a donut eraser with a note saying "Donut worry about NAPLAN"). My daughter thought that was awesome (she loves puns).