There's a game called Another Eden
that looks interesting, but isn't available outside of Japan yet (short of shenanigans to access the Japanese Google Play). It's relevant to my interests because a couple of of the staff members also worked on Chrono Trigger
(which has a pretty bad always-online touchscreen-controls-only mobile port itself) and it borrows a lot of story elements, mechanics, and graphical theming from Chrono Trigger. (see relevant posts from /r/chronotrigger
Mostly, though, the stuff I play on my phone only extends to short-session puzzle games (and Pixel Dungeon). I recently beat 2048 (in the original 4x4 grid, I'm aware there are versions with larger grids), and am close to the achievements for playing the daily Flow Free/Flow Free: Bridges/Flow Free: Hexes puzzles for every day for a year, having already finished all the free puzzles and deciding not to spend my money on the paid puzzles.
Uninstalled Miitomo recently, it's just not fun. Answering the same questions over and over gets kind of boring, and they only add outfit pieces that I'm actually interested in on a very infrequent basis.
As for the viability of mobile phones and tablets as a gaming platform, I won't say it can't work, but I will say that it's definitely not suited to some genres. In general, though, I'd prefer to have a device that's designed specifically for gaming (or, for computers, built with gaming in mind) to one whose primary purpose is something else and just has gaming shoehorned in.
In that regard, I do feel like touchscreens are very well suited for puzzle games, and this is why there's a lot of them on mobile platforms. Being a fan of puzzle games, I can't really complain.