I rarely talk about classical music to other people, but when I do I've noticed that most of them can't even name the composers Mozart and Beethoven.
It is the word "most" which troubles me here. If a majority of a reasonably varied selection of grown people really do not know the names "Mozart" and "Beethoven", then something peculiar is going on. I agree with Wolfi that the schools have deteriorated in many ways over recent decades, but what about parents ? I cannot imagine a household with such a low level of general knowledge and such a high level of parental apathy that conversations about famous people of all kinds would not have taken place many times as part of the children's upbringing. This is actually quite worrying. I guess I might encounter the very occasional adult who wouldn't know, but "most" ?!
Mind you, I was not aware of just how far the schools had sunk here until we visited a friend who teaches secondary school (ages thirteen to eighteen). It seems they have taken Shakespeare out of the syllabus altogether because he is "too difficult" for young people, and our friend reads novels aloud in classes because left to themselves the kids will not read anything at all at home.