I have yet to encounter a game that can be played with a controller, but not with mouse and keyboard.
A keyboard has like 10 times the buttons as a controller and if you give remapping ability, users will configure the game. You do not need to create the perfect control layout that fits everyone.
About the only feature a controller has, that a keyboard lacks is the analog triggers and sticks. And only if you need an accurate analog input, you will have trouble on a keyboard. Maybe throttle in vehicle games. And for something like a twin stick shooter, you have to utilize the mouse for directions.
Maybe look on /games/tag-twin-stick-shooter how those games deal with the keybord.