Stellar has nice properties, like a decentralised exchange built into the platform and native integration with existing financial institutions/other cryptocurrencies through anchors.
But I would not say it's blockchain-free. They close a "block" every 5 seconds. Depends on what you consider a block. They use boring stuff like PostgreSQL to store the data instead of reinventing everything.
The innovation of blockchains is not on the how-to-store-things side, but how to keep a state of things every nodes agree with.
Stellar can store data on Postgres because it is just a small database of how much money each account has at each ledger. Past ledgers can be erased from the database (which makes it not a blockchain in any sense anymore).
Bitcoin has a history of all transactions organized in blocks not because it's a fancy new database technology, but because that way is the way it worked out better to keep a synced state between nodes, kind of an append-only log.
You could, if you wanted that, read the Bitcoin database and translate it into a set of rows of a who-has-how-much Postgres table.
Or, better, you could implement a Bitcoin client that stored its blocks as rows in a Postgres table, but I think it would be much more resource-intensive than the databases the Bitcoin clients are using today.
The Bitcoin blockchain is a compact serialization format used as the input to the proof-of-work function. The proof-of-work is the important part, and for that we need a centrally, agreed-upon serialization format where the latter blocks inherit PoW from earlier blocks.
A Bitcoin node can store blocks/transactions in whatever way it wishes -- Postgres, Dropbox, SQLite DB on a floppy disk -- as long as it's able to deliver to nodes in the canonical serialization format, because it's needed to verify proof-of-work (and signatures for the transactions).
But I would not say it's blockchain-free. They close a "block" every 5 seconds. Depends on what you consider a block. They use boring stuff like PostgreSQL to store the data instead of reinventing everything.