Neither the baby boom, nor the huge growth of the media industry (radio, TV, recorded media, etc) after the fifties are "random".

And then there's the fact that the earlier real stars we have now (as opposed to merely people famous in the past but already forgotten) are in their 70s and 80s (e.g. the 60s and 70s musicians and actors etc, all still quite relevant for modern audiences thanks to vinyl, VHS, tape, TV, CD, DVD and cable distribution, and --something previous generations lacked until recently-- instant access to all their works and news from the streaming, YouTube and the web).

This is no clustering illusion, it's the inevitable combination of life expectancy + tons of people becoming stars en masse with unprecedented global distribution at more or less the same time that sees them now in an advanced age.