Because YT reserved /playlist and not /playlists. They also haven't reserved /watchs or /watched. People will quickly realize that /playlists loads some random channel they don't care about and will click away.
Honestly I'm surprised that YT would let users have anything like a top level path; I'd expect it to be all youtube.com/u/myuser/$FOO where FOO can be a video or playlist or whatever.
I have to imagine it's for backwards compatibility. Seems to have been a choice made in 2008[0] if not before, although new handles are primarily accessible via `/@handle`.
0: https://web.archive.org/web/20080501135434/https://www.youtu...