Fame is not necessary in my honest opinion.It oftentimes works as a distraction.I wonder how many of us have heard the name of Professor Higgs before the recent outburst in the media about the higgs boson which is still not confirmed to exist.I myself didn't.
The point is public almost totally depends on common media today to know about something.As per what media tells them most of the people only know that much.It destroys their will to self learn.Academic education also contribute to this fact.And it is certainly not in the profit book of media to publicize music composers.
Another fact that classical music didn't have a most extraordinary composer in the past few deacades who is on the level of Beethoven,Bach,Mozart,Chopin and handful of other composers.So even people who know about the famed classical composers they think that classical music is dead by now.Not all of them but some of them think in this way.Why listen to atonal music when you have mozart around?