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Unless you’re referring to storing all of this information on-chain (and not a reference to it), no it does not.

Yes that is the idea, there already are successful blockchains such as arweave that functions like this.

There's potential there. You only need to store part of the chain and there's an incentive to keep rare blocks.

But the mining is optimized for storing as big of a fraction of the chain as possible, so I worry that the future of it devolves into a few big nodes and everyone else dropping out.

It's possible to fund an immutable data archive using a normal trust. It's possible to verify immutability with traditional hashes. What is blockchain going to add?

Incentives to mine it with storage hardware and maintain the ledger with ponzi-like economics

No it doesn't you're misinformed good luck avoiding scammers out there