It actually takes quite a bit of effort to store, then distribute information precisely and broadly. There's a lot of infrastructure, effort, and money involved, and still information degrades and disappears over time.
Any libre information exists because people have put effort into it. Sometimes a lot of effort.
It’s why you can easily find literature written hundreds or thousands of years ago in multiple languages with little effort, but some memo stored in a tape archive from the 1970s is likely gone forever. “Bitrot” is more likely to be a function of diminishing interest rather than increasing entropy.
Little effort, because someone else put in the effort to keep and disseminate it. And we only know of the surviving material, we have no idea how much was lost.
Take the bible for example. It's a classic example of stories from millennia ago making it to the modern world. But its journey took the concerted effort of millions of scribes, translators, and so forth to make the journey. And it has not done so intact. We can even see how the Bible's been changed by comparing just the last two major revisions of it: NIV and KJ. Language aside, there are some pretty major ideological changes based on interpretation. And thanks to some miraculous archeological finds in the dead sea scrolls, we can see how the bible has drifted even further from its original roots.
That's not information being free, it's information degrading and being re-purposed - often re-created - for specific ideologies and beliefs.
I think that indeed, it is the inherent nature of information to radiate itself, i.e. to share (to shine, to spread)