Did you just send a link for "C:\documents\public_html\picture.jpg" (or /home/ryan/public_html) and somehow it worked? I'm in need of a history lesson because I cannot fathom how that would have worked.
No, they go with 3rd parties nowadays because most home users don't have bandwidth to host their own images.
One of the current top posts on reddit/r/funny has had over 1 million views after being posted to imgur 8 hours ago. The image file is 1.7 megabytes. That means imgur has transferred 1.7 TERAbytes in 8 hours of just that one image. That's an average of about 59 megabytes PER SECOND of bandwidth, or nearly half a gigabit per second.
Less than 1% of home users have that kind of bandwidth, and that's only to host a single image.
If you REALLY think "Oh, people only use image hosts because of the interface", you're not living in reality.
For example, I went to UTD from 2003 to 2007. This was long after the days of "the bulk of Internet users were on university networks" were over, but the infrastructure was still there. All students had ssh access to a handful of machines, the main one being apache.utdallas.edu.
So I could do this:
$ scp picture.jpg firstname.lastname@example.org:./public_html
Edit: And even if you weren't at a university, back in the dialup days it used to be that even with home internet, everyone's computer was directly on the Internet with no NAT or any kind of firewall, so you could just install Apache on your box and serve what you wanted. On paper, most ISPs banned that practice in their TOS, but it was never enforced. The real impediments were that a) dialup connections would usually disconnect if you went idle too long and b) most people had dynamic IP addresses that changed every time you dialed in (for the latter, DynDNS was a godsend). And of course dialup bandwidth was shit, so hosting anything substantial (especially an image!) would slow down your connection (seriously, people would actually buy second phone lines from their telcos and maybe even get a second account with their ISP so as not to tie up their main connection).
Broadband made it easier: even with a NAT router, you could just forward port 80 to your desktop, and you won't have to worry about bandwidth, your connection would stay up 24/7, and even if your IP was technically considered dynamic it would almost never change. What really sunk the concept of hosting your own was a) mobile (good luck running Apache on your phone, and getting port forwarding on a mobile network is impossible) and b) the rise of services like Imgur that let you host shit with no hassle (Facebook killed self-hosted personal home pages for the same reason).
It is massively convenient to run your own server. But you need to know how to maintain it (or be willing to learn). It isn't that hard, depending on what you're doing, but there's some effort and learning if you don't do this for a living.
Well worth it, at least for me.
Remember commercial shell accounts?
In the unix world, iirc, many systems were configured to expose a folder on the user's home directory (www). Which would expose that to something like: www.mit.edu/~<username>
 https://m.imgur.com/r/bicycling/b1ImCo8 with 770000 views