Why isn't chess played with flat pieces? I was wondering why Chess isn't played with flat pieces, as Shogi is, or as Chess itself is represented online (where people mostly play with flat 2d pieces, even though most sites also have a 3d theme).

Personally, flat pieces seem more clear to me, albeit less pretty. When the pieces are tall, they start blocking each other and it's not immediately obvious where each piece is.

For example, here's a simple example. This board isn't even close to being cluttered, and yet I still need to glance at White's pawns to make sure they actually are there, because they are close to being blocked by the other pieces. In particular, the f2 pawn is a bit hard to see. Likewise, Black's c7 pawn is blocked by the knight. 



I know that this can be fixed by getting closer to the board and looking at it from a top-down perspective, but... first of all, that's annoying: sometimes I just want to lean back in my chair and stare at the board from a distance in a relaxed position, yet I can't, because now all the pawns are blocked by taller pieces. Second: if you are going to be looking at it from a top-down perspective... then why even bother with tall 3d pieces? Your perspective will make them look like 2d anyway.
It's probably for historic reasons. Chess is very old and a metaphor for two armies making war, and people chose to make 'statues' to represent the pieces. Since this has worked well so far, nobody felt the urge to change them to 'tiles', that is, until computer chess came into being. I've never played Shogi on a real board, but I can imagine 2D pieces are harder to grab than 3D pieces. At least, that is my experience with playing draughts; with moves, you can push a piece, but with captures you have to pick up a piece.

But why is Shogi, which also has a rich history, played with tiles? Well, one good reason might be promotions:


They are much more common than in chess
A piece promotes to a predefined other piece (there is no choice like in chess)
In case it's captured, it matters what the original piece was


Flipping a tile is an elegant solution for this problem, unlike replacing it with another piece from outside the game.