Playing the kazoo requires being able to sing in tune. I've been playing music professionally for 40 years and have never been able to play the kazoo competently.

I think this thread is really about non-musicians who want an instrument that they can play with no effort, not about musicians who haven't had any formal training. There are a few instruments that can be played fairly easily by non-musicians (Musicmaker, lap dulcimer, kazoo, even the harp), but they still require a decent sense of rhythm and a sense of the melody as whole instead of a bunch of disconnected notes. Someone who doesn't have those things won't even be able to make the mindless instruments sound good. So maybe they aren't entirely non-musicians??

Then there are the fairly good musicians who don't have any self-critical facility. They think that because the are a Musician, they can obviously play music without practicing endlessly. I'd almost rather hear a non-musician banging on a drum; someone who obviously could be very good but doesn't know they're not is really sad.

Self-taught musicians are, if they are any good, equally able as highly trained players. Training comes in many forms. Playing along with others can be a great music school.