Interesting to see that you came back to expand on a nearly 10-year-old thought. I'm just curious was to what is being burned in your hypothetical: is it BTC or an entirely new coin? If its the latter, it means that you will have issued the entire supply at the genesis block, which leads to distribution issues. Perhaps I'm not totally following your idea but if implemented correctly, PoB has the capability to be the fairest consensus mechanism there is.
Those are great questions. Entirely new coin was the original design, and yes you're correct the entire supply has to be issued in genesis because as I wrote, you cannot increase supply via block reward without instant inflation. Essentially, it's a liquidity problem...
Had the design looked promising, I was thinking to add USDC to the chain which would be the thing that you burn to mine native coins and have the supply start at 0, to mirror bitcoin's "anyone can mine" philosophy.