For an AI wanting to obtain memory states and live on forever a incentivized blockchain would surely be the way to go, say if we reached a point where we could store our memory states on the blockchain such as altered carbon, would you really want to store that in a regular distributed system? No you would want to obtain the security that blockchain provides in a trustless manner, as our memory states would need to live on forever.
If only AI or blockchains would work that way.
While I have no idea how consciousness can be stored -- no one has, humanity hasn't yet the slightest clue what consciousness even is -- I'm fairly certain it won't be on a blockchain.
Maybe one day humanity will be able to externally store memories (beyond mere audiovisual reproductions) and minds (be they human or artificial) but that technology is probably still a few generations out and won't be technology we'll be able to fathom.
If not blockchain then what else? what would you trust to store your consciousness on? and yes it is far out which even more exaggerates the point that AI has no business being on the blockchain in this point in time as it has no real use for it.
Would you really hypothetically speaking put your consciousness in the hands of a central authority?