Earlier quoted context omitted.
That's certainly not true. P2P file transfer systems have long provided cryptographic guarantees that the file you receive hasn't been modified by anyone, even though you're fetching it from multiple untrusted sources simultaneously. Merkle trees have made this more efficient and offered maybe more guarantees, but being able to have files be transferred in a distributed fashion but impervious to corruption is not a n…
That is different use case. How would I prove that a file existed without a middlemen? I would gladly switch since the method I am currently using isn't exactly cheap.
How are you defining "middleman"? You can do this with any basic commitment scheme: take a cryptographically secure hash of your file and publish it somewhere that's either (1) trivially copyable, or (2) difficult to tamper with. Alternatively, you could do an online scheme where someone asks you for your proof and you present them with your hash after being challenged. That's a gross oversimplification, but it's the general idea.
(In general, "prove that a file existed" is not something that you often want to do in the real world. What is it you're actually trying to accomplish?)