If I pay Spotify $20 and listen to one song one, surely they don't send that artist $14...

They don’t. What happens is that your listen is pooled with all listens of all songs, and every payout the artist/label gets a check for the percentage of that total listening pool. For small artists that have relatively few listens, they don’t get almost any money.

So it doesn’t matter if Spotify passes on 70%, most artists aren’t going to see any substantial portion of that, label or not.