If there is one factor on which Beethoven's reputation rests, it is his claim to being the "universal" composer, whose music speaks to all men and women. Your story seems to confirm this assertion.
From reading music history we know that different music from the past makes an impact depending on current taste and fashions. As an example, the whole paradigm of "historically informed performance practice" was, as musicologist Richard Taruskin devastatingly argued , not a return to "authenticity" at all but a completely modern(ist) phenomenon, based on contemporary tastes and opinions.
As I live in France, I can tell you that Beethoven is nowhere near as popular or appreciated here as, say, Mozart or Chopin. Not even close. I'm speaking about both seasoned concert attendees and novices. His music's frequent accents, forcefulness, and occasional brutality is looked poorly upon. So maybe extrapolating your experience to others is dangerous. After all, it's a small sample size :)
I agree that there seem to be composers (or, more accurately, certain works) that appeal to novices, and others which appeal to more experienced listeners or practitioners. Reicha's works seem to often fit into the second category, as his works are generally "learned" and sophisticated. Therefore the subtlety is not always picked up upon by listeners who don't have the experience and/or knowledge to realize what expectations he is thwarting. To put it more bluntly, they don't really hear what's going on, and therefore underestimate the music's complexity. It's like a musical Dunning-Kruger Effect.
The larger point, perhaps, is that your idea of a typical "novice" who would serve as a litmus test for universal music is in fact an intellectual construct which has no corresponding reality in the real world. Because we are all born into a world, and a culture, and therefore our preferences are immediately influenced.
Caveat: I don't want to make the specious claim that if we all grew up listening to Schönberg we would hum his music on the way to school, that's BS. But with experience I've come to believe that assuming Beethoven's place is in our culture is immutable is probably unrealistic. In 100 years it might be someone else...