We can send the shit out of some files... if you know what you're doing (browsers retrieve tons of files all the time, for example).
It's difficult creating a service that is accessible to people who barely understand what a file is in the first place.
If all computers were publicly reachable it would be trivial to send files peer-to-peer.
I guess IPFS can be an interesting solution to this problem.
NAT punching is a thing, but it makes the implementation of p2p a lot more complicated.
The world got paranoid, as any exposed port to the raw net is seen as an invite to worms.
WebRTC exists today, and it's quite good. It's not a technology problem, it's a matter of practicality. Mobile devices being reachable over the network 24/7 is just not realistic (connectivity falls off, battery considerations, etc.). I don't want my phone to heat up and come to a crawl because the video I just shared is being downloaded by three friends over LTE while I ride the train.
The fact that files can only be downloaded once from this new service isn't just a coincidence.
Unfortunately AFAIK there has been no successful open point to point file transfer protocol that different OSes could implement and be interoperable over the Internet. Going to https://send.firefox.com/ and drop a file there is not an improvement. It's still centralized. Is there any solution to the problem of discovering the address of the sender and the recipient without a central server? I would think it's an impossible problem but there are clever people out there. Maybe mesh networks?
But yeah, some sort of ubiquitous fat client, possibly even integrated in the OS, would probably have appeared, and it would cost $50.
If it's free there's little incentive for a company to spend the money developing the easy UI and marketing it to critical mass. Even simple to use Dropbox has not made a significant dent. BitTorrent never became mainstream at the level of email but it did incentivize people to seed with the prospect of pirated content. The MPAA/RIAA have deputized any websites that accepts user content as copyright police and demonize non-enterprise file hosting services.
In a way the success of Facebook is a reflection of the spammy, phishing/malware filled, and slow nature of email and difficulty making your own website; if email continued to improve there wouldn't be demand for a modern solution. File syncing and sharing should be integrated into the operating system. However Microsoft's OneDrive and Apple's iCloud are inferior to Dropbox so a third party solution is still relevant.
Unfortunately, it only works in small groups. If you're in a large office, or need to send something to someone outside the building, you're SOL.
Well, not all the time. Never works at my parents, for example. Works in my flat about 80% of the time (although iOS 11 + High Sierra seem to be improving that ratio slightly). Never worked at $JOB-2. Doesn't work if you want to send to a non-Apple device. etc. Maybe Apple will spin up something out of the DeskConnect ashes for these cases.
When it does work, mind, it is bloody magical.