Where did the value of ETH come from?
Same answer except the index token can only get created from burning assets.
I gave like five examples of why this network has value.
Governance. Tapping into other communities. Dapps on top of the protocol that also burn the index token (or don't). Exchange fee discounts. Extreme convenience of having exposure to multiple assets with a single token. Synergy, hype, and pumps from burning the tokens of other networks. Built in scarcity due to how inflation works. Built in security without having to mine or stake tokens.
Proof-of-burn is an entirely new (yet very simple) consensus model.
Completely separate from POW/POS/DPOS.
It's basically a derivative consensus model because it depends on the security of the assets it lists.