Now imagine using that kind of technology on other day to day transactions from buying and selling of assets (real estate, stocks) to the government's activities it will give you more transparency on your deals and their actions. Someone will input/execute the transaction and everybody can look it up in the blockchain. Just think of it as an tamper proof online ledger where once you successfully inputted a data it can never be change or altered inside the chain.
OP wanted to store a PDF, at $1000 (today) to $100,000 (last December) per MB, that's rediculously expensive to do.
What you can do, is just store the hash of the file. This proves the file existed at the moment the hash was stored, and can't be altered anymore.
Dooglus did this to store Bustabit's hash
here.
opentimestamp is a good solution for proof of existence. It uses aggregation to reduce blockchain usage(spamming) in a trustless way. Thats better because a single transaction can provide PoE for potentially infinite number or files. Of course it is a little centralized, but, it is trustless, and, if you have a lot of files to PoE you can run your own aggregation pool so you are not forced to use their default servers. Take a look at
https://opentimestamps.org/ it is a very good solution.