But what would that "significant advantage" be?
That's the question I'm interested in. I don't have the best grasp of DECOR+ but for any proposal that moves chunks of block rewards around my first question is always "do out-of-bound fees upset the incentives".
Regarding the situation described in your DECOR+ blog entry, what if Bob creates his block first and Alice intentionally sets about attacking it? She would need to make her coinbase larger than Bob's to have everyone (except Bob) switch to her block. Beyond that, she would prefer not to share her transaction fees out or have them burnt. Alice would have to share her coinbase but could keep her out-of-band fees for herself.
Also there is no benefit for the client wallet, because those transactions would be understood by a minority of the miners, slowing down confirmation.
All valid points in my eyes. A client wallet could in many cases create two, mutually incompatible transactions, one paying the fee in the normal way and the other paying a slightly lower overall fee using an OP_TRUE (including standard minrelaytxfee). If there's just one miner that wants to capitalise on the OP_TRUE output then this is still a gain for the user.
I grant all of these drawbacks, but I can imagine a large enough profit incentive overcoming them. Hopefully there is no strong incentive of this type in DECOR+.