As another example, any traditional turn-based RPG can probably be controlled better on a touchscreen than a controller (navigating menus on a controller sucks)

As another example, any traditional turn-based RPG can probably be controlled better on a touchscreen than a controller (navigating menus on a controller sucks) and have at least the potential to be deep. Or roguelikes... really, most turn based games can be done okay on a touchscreen.