People have their phones with them in a lot of cases where they just can't or won't bring any accessories: at a nightclub, in the toilet, etc. If this is the majority of time when you'd want to kill time on your phone, controller-requiring games would be pointless for you.

Mind you, if you can force people to bring the accessory wherever they bring the phone, the calculus shifts. The Switch essentially is a Pro Controller duct-taped to an Android tablet; and it's a lot easier to convince people to buy one. :)

Yeah accessories are a challenge. But your comment made me think - how about a phone case that doubles as a controller? Kind of like the Surface keyboard as a phone case or protector with tactile buttons? I found a hard case called Flitchio but not sure if it made it to market and I don't like the joystick design [1]. Here's one closer to what I was thinking [2].

[1] http://www.pocket-lint.com/news/134420-consoles-beware-flitc...

[2] http://portabletech.co/