I don't know about the RIAA and mixtapes, but the MPAA tried to get VCRs banned. As Jack Valenti (MPAA) explained to a congressional panel, "I say to you that the VCR is to the American film producer and the American public as the Boston strangler is to the woman home alone."

Just wait until Disney finds out that you can make Mickey Mouse shaped pieces of plastic on an Ultimaker.

I expect part of the reason is that the genie was already so far out of the bottle with cassette tape (and even reel-to-reel) that even they probably felt that it was pointless at that point to fight. However, a number of countries did impose a fee on blank media: http://en.wikipedia.org/wiki/Private_copying_levy

Au contraire: https://en.wikipedia.org/wiki/Home_Taping_Is_Killing_Music