I got my first smartphone last summer, mainly for work, and I thought I would use it for gaming while at it. I was horribly disappointed.
I, too, wanted to use it like I used my old gameboy. Unfortunately, I found nothing of the sort. Why didn't I have a proper portable gaming console? well, I'm always traveling, and I didn't want to pack yet another device if I could help it. Having a mobile I could play on was perfect, except there were no games for me there.
My first problem was, what should I try? I wasn't gonna play from the get go, so I tried a few free games. Shitty, as you can imagine. A friend recommended me plague inc, and that was kinda fun... for a little while. I soon grew tired of its simple mechanics, but the author did get a € from me at least. And so, I ended up without games on my phone.
Later on, I got a couple android bundles at HB. Those should be big time titles, right? There should be something good, right? Nope. I actually played one (can't remember the name) about managing a spaceship, getting crew etc... Looked good. Turned out to be simplistic, minigame (QTE) oriented, easy and lacking in content. And that was the best of all the ones I tried. There was some RPG with an elder scrolls vibe, but control was horrendous. I did enjoy playing carmaggeddon for the nostalgia value, but I already own it on GOG and on PC control is a tiny bit better.
Finally I gave up completely. Recently I bought a second hand PSP and I'm happy with that.
So, do I play mobile games? nope. What would make me play? Well, for one, a decent story. Mechanics that work with the touchpad control, so probably turn based? I'd rather make it a one payment game, DRM-free. Abslutey no internet required to play, because I don't have internet on my phone and if I have wifi, I probably have a socket for my laptop too. Let me play whenever I want. And don't send me messages about zombies attacking me when I'm not playing! (I'm looking at you, PvZ2). Basically, making things play as if it was a console.
This said, two problems with this approach. 1, I'm hardly the standard target audience for mobile games, so is it worth it catering to me? And second, if you do make a game I'd play, how will I know it exists?