From a brief glance, Plex appears to be for streaming existing content. MediaGoblin is for hosting content you create.
Were I seeking a wider audience, I'd have the options of Vimeo or Xtube or Soundcloud or Bandcamp or Flickr to put my content online.
And if you don't want to turn your own content over to third parties, and thereby be subject to their licenses, and often arbitrary censorship/takedown decisions, you could use an instance of MediaGoblin to replace any or all of those services.
What's stopping me from using the dozens of web content galleries
Nothing, but if you're going to do that, you might choose to use MediaGoblin.