Were those tons of composers like Greenberg doing that sort of work at age 14?

Some were, of course (even I wrote symphonies at 14, though never published or performed). But what does it matter what age they were, unless you're talking about the ability to generate publicity? If someone's music is considered interesting only because of their age, does that really count?

Unless you mean that the fact that Greenberg wrote such pieces at 14 means that he has great potential for the future; sure, I'll grant that. But then something like the Fifth Symphony should be considered a student exercise, like the inventions and fugues he's probably been required to write in music school. (Who knows, maybe that's exactly how he thinks of it.)

Tentative hypothesis: people mostly get hooked by melody and rhythm, but classical has been exploring timbre (to the extent that it's exploring anything) for quite a while.

It's been exploring everything, melody and rhythm perhaps above all.