Exactly. There's a saying that "don't trust, verify". Blockchain is a trustless system where anyone can simply verify the ledger for the transaction's authenticity without the need to trust a third-party. A hash is all you need to verify that a transaction took place within a specified timeframe. In this case, "notarizing" a document on the Blockchain produces a hash which serves as irrevocable proof that tells you're the owner of the same. It's not necessary to upload the entire document on-chain as it would cause "Blockchain bloating" more than anything else.
For the Bitcoin blockchain, we have a service called "Proof of Existence" which notarizes any document on-chain for proof of ownership. Since Bitcoin is immutable, there's no need to worry about losing the timestamped hash on the Blockchain. Things would've been worse if the underlying Blockchain network had a very low PoW hashrate. Notarizing documents on small blockchain networks may not be suitable enough to serve as "irrevocable" proof since it's much easier to perform a 51% attack on them (effectively compromising immutability). Of course, you'd pay higher fees on the BTC blockchain just to get your document notarized. But it's much more secure and reliable than other smaller blockchain networks in cyberspace.
It's also possible to "notarize" documents on the Ethereum blockchain using a service called "Stampery". DeepVault is also good, although the cryptocurrency (DeepOnion) is not well-known within the crypto space. I believe that I can use any blockchain that's secure enough for notarizing my documents as long as I have its hash and a witness (like a lawyer) that would give credibility to the same. Countries are starting to recognize crypto and Blockchain tech as legal, so I'm guessing that a notarized document on the Blockchain would be legally accepted by a court of law.