iPhone game like A Dark Room, but...not A Dark Room?

This doesn't exactly meet every requirement, but I think it hits the primary ones. Out There is a fantastic game(found from Metafilter in fact). It does have an upfront cost but has ZERO in app purchases. You are an astronaut who is stranded across the universe from home and you have to go from plaentary system to planetary system collecting resources. Primarily you need Fuel (in the form of hydrogen and Helium(?)), Oxygen, and material for the ship/Hull (Iron). As you system hop you will encounter (randomly generated) planets. Gas giants, rocky planets, etc. Sometimes inhabited worlds. Different planets have different resources. Occasionally you will encounter abandoned ships that you can trade for yours. I think it fits what you are looking for because while it requires input, there is zero timing based inputs required. It only moves forward when you want it to. It does have decent graphics (so isn't text based) but they aren't high def and sound is not required at all. It is Single player. You will die. A Lot. So you will have to start over, but you certainly get a feeling of improving.

http://a-sharp.com/kodp/ has some similar story-about-a-civilization elements, and the turns are pretty short.

http://www.youtube.com/watch?v=bUoYUKyesDs http://www.youtube.com/watch?v=xBPsBuwiUkE

You might like https://itunes.apple.com/us/app/dooors-room-escape-game/id490611105?mt=8. It's free, the graphics are pretty light, the story is minimal, but it's a lot of fun, very easy to pick up and put down, and surprisingly engrossing. The sounds provide some hints, but aren't completely necessary. If you like Dooors, there's also Dooors 2 and 3.

Also, I find that advanced wars and pokemon gameboy games also fit exactly what your bill is. I would get GBA4IOS and play some of those games. You have to set back your device's date for GBA4IOS but because of the nature of apple phones, it's impossible for this sketchy program to cause harm to your device. Also, I really like a game called "dummy defense" which is a physics based puzzler where you try to build bunkers and stuff to protect crash test dummies. The creator made 4 or 5 games of the same theme. "Duet" was a good game that each level takes about 30 seconds, but it does take some serious concentration. You are flying two balls through a series of walls. Stair dismount and Uniwar are both honorable mentions. Not as addictive IMO as the other options. Source: I like the exact same games as you. I would love any tips for any other games you like!

You might enjoy the old-school text adventures from Infocom (and others) Download https://itunes.apple.com/us/app/frotz/id287653015?mt=8 and you can play a good number of them.

This is an old one, but http://jayisgames.com/archives/2006/08/virtual_villagers.php can be played incrementally and put down easily. I really did check the app periodically to make sure my little pixel people were thriving.

Please keep the suggestions coming - I have an endless need for amusement! Through http://ask.metafilter.com/264908/iPhone-game-like-A-Dark-Room-butnot-A-Dark-Room#3846947 I found one that is basically a Dark Room clone, but I thought would be right up the collective MeFi alley: http://bloodrizer.ru/games/kittens/# (warning: your kittens will likely not all last the first winter).

Not for the iPhone yet, but the first to come to mind is http://forums.toucharcade.com/showthread.php?t=4270.