Youtube became big before hosting video became in any way approachable for a small operation, it was a VC-funded project to corner a market incurring massive operational losses and then they got bought up by google who funded further massive losses and now they're trying to cash in.
I mean it's not like we didn't torrent back in the days but noone thought about building a creator platform out of it.
Where you download an episode and then listen to it? Likely due to bandwidth restrictions, early file formats, and hardware limitations.
The first issue, bandwidth limitations, results in the download taking a very long time. Video takes up more storage and therefore takes more time to transfer the data. People may become bored, run out of time, or need to pause the download and restart it later. Faster connections help, but...
Many early video formats did not handle partial files well. You needed to wait to download the entire thing to watch it. Some formats can break the file into smaller pieces and reduce how many you need to download at once, but then you need hardware to piece the final thing back together seamlessly.
And the limit on hardware that can piece together the video files in real time limits the accessibility of playback. You also need more pre-processing to get the videos into the right format.
Better hardware just pushes the issue to bandwidth. Bandwidth improvements push the issue to the storage hardware. Better formats improve things for hardware and storage, but usually at the cost of quality.
This is a great point, not sure why you're downvoted. Something else I thought of is the fact that YouTube is very good adjusting streaming quality on the fly, meaning unless everything is pre-cached it would be difficult to stream the way most podcast apps can "stream" audio by essentially downloading it faster than it can be listened to.