Pastbins (plural!) are very unstable websites. No single one dominates the scene, the show up and go offline constantly.
You can put a webpage into the URL by compressing it into the PATH (the part after `?` eg `example.com?<html><title>URLs are my Host</title></html>`
That makes all link shortening/bookmarking sites pastebins. If example.com has JS that expands and displays the document, then the user gets a good experience.