Yes, giving choice on controls is better, you can totally do that!
Yep, why not.
I'll play on PC and it won't feel as a 2 buttons game to me specifically :D but it'll be ok pour mobile players!
In the end anyway, it's always better to offer alternatives, you can assign all the keyboard AND joystick buttons, and so on, as long as only 2 inputs are need to play the game.
I mean that if the key "A" and the Mouse button 1 and another input all activate the same effect, it still counts as one button.