As far as I can see, this only concerns coin generation.
Yes that's right. You would still likely need a "consensus layer" blockchain for the trading of the coins. But I think something special happens when you A. Have a separate but truly fair distribution method and B. have an incentive to mine consensus blockchain for free (protect your investment). The special thing becomes that people mine the consensus layer blockchain for no rewards. So people will "Coin Claim" mine for coins and they will "Consensus Mine" for free to protect their investment (kind of like how people run their own full nodes when they don't have to). This means the maximum amount of coins can be limited if desired (I always think supply should be infinite though) but that fees will never be necessary to incentivize mining. The consensus layer kind of becomes disposable and less serious. What matters is your own backup of your coin's claiming private blockchain.
PS: I added a new whitepaper link to my original post which gives an example of a more mainstream acceptable way this may be done.