Thank you for your suggestion! They're great for when you don't have a controller (with you), but as I bought the Gamesir X2 Pro just recently, I would even prefer suggestions for games that are specifically not touch only :)
I think most turn based RPGs play great on touch devices. If you don't have a controller, it's fine because fine-tuned controls usually aren't that necessary. They're also usually meant to be picked up and set down, meaning you can grind a few levels while you're just chilling on your phone or something.
I recently acquired a GameSir X2 Pro (it's still on its way), and I downloaded some games that I've always wanted to play and/or looked interesting.
Among the ones I'm most looking forward to playing are God Of War (PSP and PS2), Resident Evil (1 on PSX as I love the franchise but never had the opportunity to play 1 decently) and Code Veronica: X.
Prince of Persia, ICO, DMC3, Genji, DBZ Budokai Tenkaichi 3, Onimusha etc. Almost all of PS2's popular library is in my phone's memory.
I'm also looking for a recommendation, but this time I'm looking more around the PSP or maybe GameCube/Wii. I tried to emulate the Vita on my Poco X3 Pro, but with little success it was more than worth the effort.