I mean Chrome and Firefox are user agents too, which can also access YouTube's content.
Their sole purpose is not saving the content, they provide functionality to do so, but they are mainly meant for emphemeral viewing, not downloading
Yes, so my idea would be to make youtube-dl a tool for viewing content without annoying ads and it could be extended to be a download tool (in another project, operating in a more gray legal area).
This means that most developers in the project could contribute in a completely legal way.
There's no legal distinction. It is a user agent, it's a web tool (agent) acting on your (the user's) behalf.