Information never is and can't ever be scarce. Valid moves in the game are scarce, as the playing field is limited in time and space. Information can never be owned. It can only be kept secret.
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The data preserved by Bitcoin is NOT arbitrary. It's deeply meaningful in the context of the game, which is bound by non-arbitrary physics.
Adding arbitrary data will always suffer the Oracle problem, which is to say "bananas on the blockchain." It doesn't solve anything.
Determining what bit sequence is valid via physical constraints is what makes bitcoin real, not a simulation. It's what makes it ELECTRONIC cash, not merely a digital construct.