Mahjong board formation and drawing rules
In theory yes, you can play with a single pile. The reason people setup the wall this way (aside from historical reasons) is because the layout suits the nature of the game. You typically play on a square table and tiles are fairly large so stacking them in a single tower would be pretty dangerous. Also, after setting up the wall, players draw their hands from the wall which is done in sets of 4 tiles at a time going around the table. The layout makes it easy to draw the tiles, while also encouraging the social aspect of the game.