I like them a lot
New Chaturanga pieces
Hi, nescitus! I was thinking about the same stuff, but really I didn't want to bring it out just yet, because in my opinion the staff is doing a nice job with variants and didn't want to complain about stuff just yet, especially after the Chaturanga-Giveaway update.
Here are my thoughts on it:
In general, replacing some pieces is a good idea for me.
- I also like the new Ferz. Unique design that I've not seen anywhere else really, and helps for the "pointy hat = queen" problem that beginners seem to have.
-The Chariot. Well, to be fair, I see the thought behind it: the Rook was initially a Chariot and anyone who appreciates the history of a game (like me!) can only smile when seeing the Chariot. I believe it helps with immersion and gives a feeling of uniqueness to the game. It really seems like you're playing the original game.
HOWEVER, I do agree that they are a bit confusing. I myself needed some games to really get used to the new visual and it still kind of messes with my board perception. This might be something that will fix itself once I've played more with the new pieces.
- The Elephant is so cool. I really do like it. But just like it has already been said, it messes up with my head real bad. It's just too similar to the Knight. The fangs and trunk aren't enough. I'd say the Elephant is the main problem with the new set. Like I said with the Rook, I love the thought behind it but the execution is subpar, unfortunately.
- Another issue I have is incompatibility with other sets. I usually play with the "Classic" piece set and this is the result: 
Bleagh, awful.
The problem isn't there when playing with "Neo" (actually looks quite good aesthetically), with "Alpha" it's even worse than "Classic".
SUGGESTIONS
My solutions for the current issues would be:
- to integrate the current pieces within Neo, and to reverse the changes in the other sets. Let people choose if they want a Rook or Chariot.
- a redesign of the Elephant. I'd say the main problem is that the Elephant is facing left, just like the Knight, and the morphology is just too similar. I would advise flipping the piece to make sure it looks towards the player's right (a frontal view might work just as well if not better), and to design a sprite that is unmistakable for a Knight. If a later view is chosen, then an upward pointing trunk is a must.
Some possible inspiration:
-https://www.flaticon.com/search?word=elephant
-https://commons.wikimedia.org/wiki/Category: (inserting spaces cause smileys) SVG_chess_pieces#/media/File:Chess_ell45.svg
- 
I'll conclude taking the opportunity to thank the mods for their work and for listening to feedback <3
Flipping elephant may solve the problem. I appreciate the idea that it should not look like a bishop, because it confuses beginners as to its strength. But neither should it look like a knight.
As mentioned by Arma55, I do agree with the statement:
"anyone who appreciates the history of a game (like me!) can only smile when seeing the Chariot. I believe it helps with immersion and gives a feeling of uniqueness to the game."
Agreed 100%.
And as a beginner myself, indeed, new pieces helps a lot not to get confused to its strength as mentioned by nescitus.
Congrats to chess.com developers for this update! Some minor adjustments might be indeed welcome, but its not confusing. It is just a matter to get used to it. We all got used to FIDE chess and its pieces at some point. I think it is always positive to be open minded and not let your brain get lazy to learn new board perceptions.
Do you like new Chaturanga pieces? For me they transform once-familiar board into horrible mess.
- new fers is fine, visually dissimilar to a queen, and it may prevent beginning players to think of it as a strong piece
- there's absolutely no point in replacing rook witch a chariot - it just destroys important visual cue.
- alfils are catastrophically bad, their shape is too similar to a knight. Today I both blundered a piece because of that and got a 1750+ player to blunder his, because he considered a square to be defended.