One use-case scenario for 13 button controllers is a leverless controller that has one extra button for your left middle finger in an optional WASD layout.
The T series of Haute42 controllers comes in 16 or 13 button versions to suit your fighting game preferences.
The Battle Grid is an aluminum controller with 13 buttons in a split layout and a bigger screen than usual.
If you dug CieloGames' 13 button layout—as well as its iconically steep slope—then you may dig the FusionFlex V3.
The FusionFlex V2's extra index finger, thumb, and palm buttons may be the very reason that you win the next Evo.
You can buy Akekon Dojo's DP-5 regular or mini version with 11 or 13 buttons and at least three color options.
If New York is the concrete jungle where dreams come true, then the NY-box may be the controller that'll fulfill your dream of winning Evo!
You can choose the color of the small & light KBGM-H06M, which also features LED for its buttons and midsection.
Cubs made a hybrid, the Cubstraption, that has a GameCube controller on the left and half of a box controller on the right.