I am with you that there are other solutions, but they are not easy to use for enterprise customers and that is where FTP still thrives. Rsync? Sysadmins maybe know this, but your marketing guy? BitTorrent? That's for illegal stuff and it is blocked on our company network.
You want to send a client (e.g. a newspaper) all your fancy videos and graphics (remember you are the marketing guy) to publish somewhere. The videos are of course 4GB per file.
What is the easiest way to share these files you have sitting in your "Marketing Campaign 2016" folder? Ask your IT department (just going by your suggestions): - HTTP? Our server cannot handle file transfers larger than 2GB and times out after that. Also most clients don't have resuming capabilities. And don't even start with public file sharers our data is private. - BitTorrent? Is blocked on our network. Also the client told us it is blocked by their ISP - rsync? What is that? I'm a windows guy. Also I doubt that the newspaper will know what to do with some weird command line commands...
Just set up a quick FTP server (or use the existing one) and send the link to the client. Everything works. Resuming. Large downloads. Easy to use. Reliable. "Known" interface as the client just sees folders and files. Many clients available or just the web browser.
I am not surprised at all that FTP is not dying, I myself have often advised customers to "just use FTP" instead of whipping up a custom solution. It just works. The cost is low, the benefit high.
Sadly there currently is no run of the mill solution to replace FTP that "just works" for the average joe.