I think it would be possible, even though it isn't happening now. But even if it were to happen, we'd have to keep in mind that it would be a lossy compression.

Relevant to btc, now that I think about it, as a kind of one-way function. In the theoretical limit case, which we could only asymptote toward, you could "hash" all possible information into the price; but, given the price, you couldn't reverse that process and understand the thing in anything like its full complexity.