This game that I just played is a great example of how 2nd = 0 works very well. https://www.chess.com/variants/4-player-chess/game/27692772
Red starts pushing forward into my position. At some point he must stop and let me consolidate so we can weaken green. But he doesn't he keeps coming so having the option to bail out works very nicely. It's too risky here. If I allow red to promote again he may continue the attack further and I can end up 3rd losing maybe - 15 and the fact that I'm stopping him promoting is making him more frustrated. There is no way back here and it benefits me to settle for 2nd. So at low rating levels this works very well as you cannot be sure what players will do. The question is whether 2nd = 0 would work for high rated games too...
I think you made a great decision by playing for 2nd here. This does illustrate my experience of playing for 2nd being a viable backup strategy in the three-player stage.
The 2nd shouldn't be neutral, it has to be negative. The 2nd player is in fact the MAIN loser usually. The 4th shouldn't be punished a lot. The difference between 2nd and 3rd and the one between 3rd and 4th shouldn't be huge.
I somewhat disagree with 2nd place being the main loser because I have easily put foolhardy teamers into 3rd place in my past games when my opposite was really bad and goth 4th place.
I do think that 4th should be punished a lot because there are effective strategies, such as betrayal, to prevent a passive opposite from forcing a player into 4th.
I do think that a difference between 2nd and 3rd could help to address some of the issues you bring up. Again, I think that there is nothing wrong with 0 for 2nd because it is only players who don't play to win who continue to team with their opposites, meaning that one could put such players in 3rd.
Are your concerns primarily aimed at those who foolishly seek to team to the end and have opposites who do not punish this?