Elo also work in multiplayer games, not only one-on-one games.
Elo is not a very good metric for Hanabi, sure. but it is a good enough rough estimate for skill level anyway. It is an artificial comparison to some arbitrary scores: "If the player average is x and their score is over y, then we calculate as if they won the game collectively. If not, then they lost so they lose collectively".
There should be some kind of score calculation for the game so that the players could tell if someone is good in the game or not. Elo is currently the best thing we have. And there is no need for anything better anyway. It's a rough estimate and that's it. You should not take it seriously.
Elo calculation or Hanabi takes the average of the players because even if you are a strong player, the lower elo player could mess up the game for both of you. So you as a stronger player can win as many points because you got over the "handicap" of the weaker player in your team.
You should not play the game trying to increase your elo at all. This is what you seem to try to say. It's a pointless metric and you should not think so much about it. Just play and get better at the game in the long run.
Lost points being more strong is a feature. This is how Elo works when you reach your skill level. Elo is not meant to increase indefinitely. Winning is already quite easy so you win less points. But losing happens less often so you have to lose more in order to balance out the winning point increases. So losing more just balances it out.
The challenge in Hanabi is not to gain elo. Playing with people at your skill level is the most fun as you can develop more and more efficient tactics. Actually, you stand to gain more points if you play with people of smaller elo - if you win then, you win more, if you lose, you lose less... as your average elo is lower. At 1000 average elo, you basically gain 0 elo even if you win.