Fun fact: I actually thought this is how all rollups work until about a year ago 
I guess because it’s a quite inutitive solution.
I have a question about the “anarchy” part. You said that wasted computation can be avoided by the based sequencing but this is not obvious to me. Even in PBS, wouldn’t you have many builders compete to mine the next L1 block, and hence all repeat the effort of making the next L2 block as well?
I’m thinking specifically, all of them would do the compression work, and all of them would have to compute the validity proofs. (Am I missing any other work?) You said that the latter can be avoided if the L1 builder can validity-prove the previous block, but how does that change anything? Then the competition for proving block n would simply go to block n+1, it wouldn’t disappear.
Thank you