IMO, one of the interesting aspects of this concept is that it furthers decentralization. Though one concern I haven't worked through is whether a nefarious actor could control the "blockchain" if they just continued to transact, being willing to part with some % of their money in fees in exchange.
I think it could be done entirely without fees, just using valid proof of work as the means for verification.
Fees lose their structural role when the verification is done 100% p2p, because the incentive for the participants to donate proof of work is so that they can use their money the same as all others. And DAG fits the real world usage model; provide the proof of work when it is needed, i.e when the participant wishes to make a transaction. It almost sounds to good to be true though, so I share your cautious optimism, which is why it needs examining. The idea is deserving of it.
Hrm - this means I haven't fully digested the research done in the OP. In my imagining of this, the verification is still "crowdsourced" and not directly p2p. I.e., when you make a transaction, you're also making a block candidate, with your transaction "on top". If you're POW fails to meet difficulty, your transaction/block candidate hybrid joins a pool of other failed block candidates. (or one can imagine a temporary failchain, but this might be similar to the DAG). Once a successful POW is obtained, that block candidate is accepted into the blockchain, and the other failed candidates are cleared (or if they are linked on a failchain, they naturally clear). In this version, you prevent spamming the work-space (like is currently done with bitcoin) by forcing every POW to include a novel transaction.
I know there are holes in the above. So I should go back to trying to understand this DAG thing.
But indeed, as you say, if you remove the fees (or the any blatant incentive for supporting the network), then there's no incentive to spam the workspace.
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