So many possible games and vulnerabilities are opened with something like this. I'm not saying it isn't worth thinking about and doing, just that it needs to be designed and tested very carefully before allowing it to affect either content/curation payout or witness scheduling.

For example, the last time I was thinking about designs for curation delegation I got overwhelmed by how the design needed to be sophisticated enough to prevent games that allowed a user with a certain amount of Steem Power have multiple times more influence than what their SP would normally give them simply by sequentially changing their delegation of curation influence to their various sockpuppet accounts over time and allowing those "unique" sockpuppets to all cast their unique votes on the attacker's own posts which would give them very nice rewards. I'm sure the Account Rank algorithm will need to be designed very very carefully to avoid games like that as well.

Regarding the computational cost. At first glance it does seem like it would be very heavy to do something like this. But also, I don't agree that it necessarily has to be broken up into chunks that can be completed in less than a block interval. If you allow the Account Rank weight/reputation changes/effects due to operations on the blockchain to be sufficiently delayed, you no longer are limited to single threaded computation. Those calculations can be done in parallel with normal block production, and the outcomes of those calculations are then expected by the consensus protocol to be incorporated into the database state at some fixed number of blocks later.

Using the Account Rank algorithm we could replace and eliminate the overhead associated with tracking and tallying witness votes. Instead the witnesses would be the top accounts by Account Rank that didn’t opt out of being a witness.
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Each user would simply add their 30 most trusted curators (aka friends) to their account and the Account Rank algorithm will automatically distribute influence among the friends.

Distributing influence over curation (i.e. deciding how content/curation rewards are paid out to various post) is very different than distributing influence over selecting block producers. The people I would trust to do a good job reliably operating a node (or even the people I would trust to select the people running the nodes) are not the same people I think produce good content on Steem nor are they the same people I trust to curate good content. And for that matter none of these people are necessarily the same people who I think are just the most trustworthy individuals period (in a web-of-trust sense). I want more separation of power / roles, not less.