Yeah, but there was a
reason that we "didn't have much else in the way of video on the internet" at the time — bitmapped videos were far too bandwidth-intensive for most people to download
in realtime. (You could still download them, and people sometimes did; but a 3-minute, 240p MPEG1/RealPlayer clip was something you'd need to dedicate a half-hour to fetching, either using a download manager or Limewire. It was
not a "click to play" experience.)
This was also the reason that YouTube didn't get started until 2005 — that was about when at least some people were starting to be "ready" to receive streaming bitmapped video over their Internet connections, without needing to make a big production of it.
Flash as a distribution format for video was distinctive and successful because it was essentially a standardized abstract machine for demoscene demos — a Flash animation wasn't a video, it was an ActionScript program that rendered a video when executed. So a Flash animation could be arbitrarily lightweight on the wire — as long as the author was clever about composing things out of vector bits and small reusable textures.
Flash as a distribution format for video was obsolete basically as soon as people's Internet connections improved enough that they could just stream the pre-rendered output of someone else rendering out the Flash animation program instead. (Which was around... 2010, I'd say?) Which also meant that, at that same moment, the "Flash aesthetic" of vectors and reusable resources basically instantaneously ceased to exist, because it had all been in the name of conserving bandwidth, and there was no longer a reason to do that if you were rendering the result out to MPEG anyway.
Flash as a distribution format for games stuck around a few more years, because HTML5 wasn't fully there to replace it yet. And the authoring tool (now Adobe Animate) is around to this day, because it's still an excellent tool for creating vector-based cartoons... that you render out to bitmapped video.