There can be proof-of-stake blockchains, proof-of-use, proof-of-minimum-aged-time, etc. etc. The blockchain is just a chain of blocks, there are innumerable ways to protect it, verify it, and distribute the data.
I think the core value of a blockchain (as opposed to any general database) is that the most recent blocks contain a hash of the state of the system up to that point. This provides a tamper-resistant historical record of what's occurred previously.
I think your second point is what some of the critics of the bitcoin obsession are talking about. Not every blockchain needs to be as attack-resistant as the bitcoin network. Many of the speculative blockchain uses like for the Internet of Things could benefit from a history of all transactions but don't depend on it. Proof-of-stake might work fine for many cases.
What you are describing has been a core of any ledger/immutable database. It isn't new and in fact has been around for ages. You don't really think a bank keeps all you money in a sacred database cell do you?
Plenty of banks use pretty horrifying technology. Append-only databases have been a cool research project for ages but I've never seen one in production.
They're more likely to use mainframe database systems with the verification done in apps that interface with it or do batch runs on it. The mainframes and databases themselves cover the integrity and availability portions. So, it's a ledger in practice but not directly stored as one.
Matter of fact, storing it as one is incredibly wasteful. Banking systems have shown it's not necessary. Just need the transactions, timing, sources, and verification of them.
Are any of those dividend-paying companies? At the risk of no true scotsmanning, I wouldn't count it as "production" if the company isn't making money off it yet.
Or a series of files with numbers that go up and a data structure tracking their dependencies. Git and others might use Merkle Trees but they're not even necessary. Good, but not necessary. Lot of ways to represent these basic concepts with so many tradeoffs.
That's why it's exciting when people break away from the crowd dictating specific approaches and start asking themselves questions about alternative techniques. :)
That problem was solved back when we started putting money into banks and using it with computerized transactions. Variations on that model with nonprofits and distributed transactions could go far as alternative go current system.
