Yes.
Poll: Who thinks there should be a meaningful difference between 2nd and 3rd place?

You may not realize it, but you answered your own questions of why 2nd = 3rd is the best option. We considered many points systems and combinations when creating the 4 Player Chess League.
If 2nd = 0 or + points, this would encourage Teaming, and throwing in certain scenarios, and you're more likely to Team with your opposite from beginning to end. I'm not convinced the current system is best as I've experienced and witnessed a lot of betrayals, but that's just the nature of Solo since 2nd - 4th all lose points.
If you and your opposite took out a flank, which is your strategy, then you 2 are more likely to win, which means opposites would be more likely to Team against the other flank in the 3 player stage, making it more of Team's mode throughout.
By having 2nd and 3rd losing points equally, it encourages everyone to play for 1st in the 3 player stage.

People understand the importance of having last place lose the most points as an incentive to play the best you can and not get the least points. Also the satisfying feeling you get after taking out an opponent and avoiding the big rating loss of last place.
Gold, I don't agree at all, at all with that.
That mainly creates the incentive to play "to avoid being 4th at any cost" and it significantly decreases the risk taking and the overall quality of the game. Punishing 4th too much is a clear mistake from my point of view. The incentive in any game should be "play to win", not "play to avoid being the worst player".
In addition, VERY OFTEN you are 4th without having done anything wrong, especially if you're green, simply because you have an incompetent player in front. Doesn't make any sense IMHO.

1. As far as I am concerned if you earn more points, you played better
VERY OFTEN it's not the case at all. Quite often you're 2nd simply because SOMEONE ELSE played much better and created opportunities for you to exploit (you eat, you earn points... you mate, you earn points...), and then in the 2nd stage you play badly and lose, but still have more points than the 3rd THANKS TO HIM precisely.
My observation is quite the contrary to yours: the 2nd is in fact the MAIN LOSER most often, and very often the 3rd played better, but lost to 1st because of the 2nd incompetence, in the 2nd stage out of the three stages of a FFA game.

It makes sense if you think about it, the people who lose should be equally punished. Ok one of those players may have played better than the others, but it is impossible to determine who that will be (4th, 3rd, 2nd,), or to determine who played the worst out of those players. Also, solo encourages opp-loyalty and solo is also way more interesting and tactical, and everyone is trying to win instead of avoiding 4th.

in first place i cant understand why they have removed the different modes FFA and solo.
are 2 totally different type of games, in FFA it should be totally fine to team up with someone as the game evolves, to try reach the best place you can reach, meanwhile in solo only the first place count and there's no difference between 2nd or 4th, so you only play to win and nothing else.
and to be clear i prefer the FFA philosophy, where each position make a difference, BUT i strongly would like to have back the split between FFA and solo modes

https://www.chess.com/variants/4-player-chess/game/32003608
Games like this are why I HATE the idea of 2nd and 3rd losing equally.
I agree with GoldCoinCollector, the rating seems rather frustrating, and also the frequent server disconnects. There must be a reward for weak players or newbies to come in 2nd place.
Also why not let the players decide between two ratings systems. There is enough 4PC games currently, with the waiting time being a few seconds only from my experience.

in solo u have 1/4th win rate in team its 1/2 team is better
actually in solo and teams its the same win rate if you play at the same level - 0%. In solo, although its 1/4 win rate, if you lose 3 times, your win on the 4th will make up entirely for the previous 3 losses. In teams, you win as much as you lose. In solo, you win 3 times more than you lose.
I would like to start off this post by stating that I am very glad that the rating system has been updated to have last place lose the most points. I was not at all surprised that players voted the solo rating system out as it was widely disliked. People understand the importance of having last place lose the most points as an incentive to play the best you can and not get the least points. Also the satisfying feeling you get after taking out an opponent and avoiding the big rating loss of last place.
That being said, I still very much dislike the fact that 2nd and 3rd lose equally. I understand the rationale for why 2nd place was no longer awarded + points. People taking the lazy route and ending the game early to get 2nd and a 1st place winner throwing away pieces to usually their opposite or whoever helped them get 1st ( a pretty scummy thing to do to cheat someone out of a hard fought 2nd place victory even if it was well intentioned to reward someone for helping you get 1st ) etc. But I will list what I see are the important reasons for there being a difference between 2nd and 3rd place.
1. As far as I am concerned if you earn more points, you played better and should be rewarded accordingly. That is taken away if ANY place loses equally.
2. People need incentives to stay in the game as long as possible. I have posted before about a handful of games that I have had where I hemorrhaged material early on in the game, but managed to stay alive with only 1 or 2 pieces left and was able to be an asset to my opposite ( or it could be your right or left opponent as well) and managed to pull out a 2nd place victory. There was no path to 1st save a series of unlikely blunders from the other players, but there is a path to 2nd with the right play.
3. Related to point 2 is that there does come a point in the endgame with 3 players left where 1st is no longer possible for 1 or 2 players, but they can get 2nd by teaming up at the right time with the player who will win. One of the key factors in 4PC is mutual benefit. If 2nd and 3rd lose equally, that is lost.
On the issue of how to dole out the 2nd and 3rd rating points if awarding + points for 2nd is permanently off the table, then why not have 2nd lose 0 or only 2-3 rating points and have 3rd lose 4-5 if 2nd is 0 or 7-8 rating points if 2nd is 2-3?
So those are my thoughts I would like to hear all of yours. The bottom line is that I really HATE the idea of any place losing equally. It leaves me with a very unsatisfied feeling.