Non-edgy content is not going to disappear, heck it might even be quite popular! (See: Hallmark Channel in "traditional TV land", the appeal of things like cute animal videos in "Internet land") Edgy content is nothing new, either, although of course what is "edgy" changes from generation to generation.
Youtube's problem as I see it is differentiation. Howard Stern was "edgy" for his time, similar to how some Youtube producers are "edgy". Yet he has no problem attracting advertisers as far as I know (Googling suggests his radio rates in particular were quite high). But it seems like it was/is much easier in traditional advertising to say "I [do / do not] want to advertise with Howard Stern" then it is to say "I [do / do not] want to advertise with PewDiePie". That's really the crux of the problem as I see it, it flat out sounds like Youtube can't do targeted marketing very well (a ding made more painful considering this is the success story of Google Search). Heck, "I do not want to advertise for ISIS recruitment videos" seemed to be a request Youtube couldn't fulfill for a while.
I don't think "edgy" in itself is a problem to many advertisers per se (except for certain step-over-the-line moments) and I agree with you that Youtube is tackling things in a way too crude manner.