I think you can make DAG work but you will end up with divergent partions that can't be remerged
Why? If there are no conflicting tx's, someone can issue a tx referencing 1 tx from partition 1 and 1 tx from partition 2, et voila.
Due the quoted Prisoner's Dilemma that I outlined (for which I believe your response was inadequate for the following reason) in that no one has an incentive to be first to lengthen the tips, the game theory is going to devolve to everyone agreeing to blacklist double-spends without actually abandoning branches containing conflicting transactions where they have transactions.The Prisoner's Dilemma is only solved in favor of lengthening if double-spends won't cause a branch to be illegitimate. Thus the branches will diverge while they lengthen. Your preferred algorithm will not hold over time. CAP's theorem is guidance, and now you just need to model it or put it into the wild and observe.
You might try to formulating some fencing or "longest-path" algorithm, but you are just going to end up back at a block chain (giving up Partition tolerance) once you have solved the Consistency and Access issues.
Any way if I am wrong, then kindly be the first to disprove the CAP theorem. Good luck with that.
If, for example, I'm a merchant who accepted a payment in the "smaller" branch, then I have all the motivation to do some more PoW to make the branches re-merge and therefore increase my safety. And please stop randomly citing Big Important Theorems that have only a vague connection to what we are discussing. In academic circles such behaviour is not welcome.