Most people who want their works to last forever want people to read and use and enjoy them. Burying and having it forgotten doesn't meet that criteria.
Making millions of copies and burying some, with incentives for future people to make more copies and bury some again seems more likely to succeed.
And the blockchain isn't far from that.
What you're essentially doing by putting stuff in the blockchain is tricking people into copying it millions of times. It doesn't mean any of them will read it or appreciate it. I agree with your analogy, but what's the point of it? Some weird desire for your footprint to be larger and imposed on people for all time? I can't think of much more narcissistic than that.
Wars typically are as much about spreading culture as they are about genetics. Religious crusades are a way to spread culture without genetics.
Humans seem to have a desire to increase both their genetic and cultural footprint into other humans. Make sense really - expansionist traits tend to survive.
The oldest known poem is 4000 years old and carved in clay. It seems to me if you want a poem to last forever, never to be seen, there are much better ways, like carving it in granite and burying it deep underground where it's unlikely to be found.
Even if you insisted that it's "digital", making a commit in the Linux kernel is much more likely to last for as long as computers last because Linux is actually useful, sustainable, and copied to just as many, if not more, computers as any blockchain.