JSR for iOS and Android played quite well, so I could see a new game made for the mobile platform working well.
As far as shmups on touch screen devices, I have played a few made specifically for iPad and they play amazingly well. You just put your finger at the bottom of the screen and the ship hovers a few inches in front. Holding down fires (because when are you NOT shooting in a shmup?) and moving around your finger has the ship match that 1:1.
I'd also point to the 3D Classics Space Harrier, the stylus controls were similar to this and were amazing. Have the bottom half act as te track pad and the top half act as the screen.
Raiden has controls like that too, and it's still terrible because of one issue you cannot avoid: Your finger is covering part of the screen constantly. Sure the ship is 'In front' of your finger, but you need to be able to move up and down as well as left and right. It's terrible unless the game is dumbed down to the point where there is zero challenge anyway.
I've tried playing Raiden a bunch of times with various control methods on phone, because it seems like it would be the perfect quick bus ride game, but it's frustratingly unplayable each time and I end up not touching it. Lucky I got it in a humble bundle. I'm not convinced Shmups can work with touch controls sadly, because it would be great if they did.
Dividing the screen into the track pad and game might work better since you're not covering the screen with your finger constantly, but then you lose half the screen...
As for JSR working on iOS, I'd be interested in seeing that, because even a game with plodding pace like KotOR handles sketchy with touch screen running about, and that's just exploring the hub world. I can't imagine JSR being anything less than headache inducing with touch controls.
I just had a look at a demo and it uses a 'virtual analogue stick'. I personally find those abhorrent, having played a lot of emulated games on my phone with virtua controls they are usually borderline unplayable. Again a big part of this is that your finger covers a big part of the screen, unless you're playing on a tablet, in which case WHY? Just play the DC/360/PC any number of good versions with real controls!?
Has anyone played a lightgun style game on touchscreen? That seems like it might work, but literally touching the screen would kill any challenge for the game, or most of it at least I would think. Otherwise HotD might work. Maybe you could alter it up so it's more about hitting specific points or just more enemies on screen? I know that SNK made a lightgun style shooter recently, but it looks atrocious. If nothing else Sega could do a lazy port of HotD 2 and 3 again or something.
As far as monetization goes, Sega could make you pay for bullets per day (or health or something. Similar to paying at the arcade) as well as some sweet extra playable characters. Ulala would be my pick (she already has a lazer gun after all).