Given that, bitcoins are not property, but information
Why can't information be property?
Information is inherently free, we can make laws that make it property, but it has characteristics that property doesn't. You can keep it safe by presenting it from spreading by keeping it a secret, property on the other hand is kept safe by protecting it physically. To make Information property you have to take the meme or ownership and apply that meme to the concept of information, it is intellectually dishonest, and as the internet is highlighting somewhat impractical to enforce.
I'm catching up so if this post is repeat forgive me this just jumped out out at me.
To say information is free would be a fallacy. Information is in fact a commodity. There is a considerable investment made by anyone wishing to learn whether it be time, sacrifice or monetary. Information is very expensive, and highly valued by those who know how to use it.