While such a scheme might solve this particular method of storing data, it won't make the general problem go away.

For instance, if I want to publish an 'n' byte message, I could generate 'n' wallets, each having as their final byte of their fingerprint the n'th byte of my message. Constructing 'n' such wallets will require on average "256*n/2" units of work---quite small, all things considered. I can then transfer a single bitcoin to each wallet in turn, forming a linked list of the bytes in my message. Even better, I also get my coin back at the end.