Sounds like you'd be fine with a flip phone from 10 years ago and a small high quality camera. You don't seem to be the target audience for the latest smartphones.
About 4 years ago, Sony Ericsson made an Android 2.3 phone called the Xperia Ray. It had a 3.7" 960x480 screen. I used it for 2 years (and again for another year after I broke the Huawei P6 I replaced it with). By the end of that time, it was really past its useable life. Not on account of build quality, battery life, or screen realestate. In all those respects it was fantastic, and still perfectly functional as a feature phone.
It started life as a perfectly servicable Android phone. A little on the slow side, but not drastically so. The main problem was its 384MB of backing store. By 2015, very few Android apps supported installing to the SD card, and Google Play Services managed to eat almost all of the available storage.
Ideally, I'd like a modern phone with the same size and build quality of the Xperia Ray, the phone that fits unnoticably into my pocket and survived countless falls onto hard floors. I don't think it even needs to be super fast. Just with enough backing store to function as a modern Android device.
And knowing that such devices are possible is the reason I don't agree with the "you'd probably be fine with a feature phone" answer.
At the moment, I'm using a Z5 Compact. It's a great phone with solid build quality, but it's still too big IMO.
Quite a lot of people have asked me about a small but powerful Android phone, and there are none!
It's incredible, but all companies go in the same direction. In the very few instances when they do innovate, they go in really odd directions (curve displays, in-built projectors), but they don't address basic stuff like size or physical keyboard.
I switched to iOS for this reason - the iPhone 5/SE form factor is smaller than every Android currently on the market (and running a relatively recent version of Android).
My SE is 124 mm x 57 mm x 7.6 mm. My previous phone, a Moto E, was 125 mm x 65 mm x 12.3 mm. The Xperia X Compact mentioned in another comment is 129 mm x 65 mm x 9.5 mm.
I'm considering buying an Xperia X Compact. It's about the size I think I'd be happy with, Sony devices tend to have great development communities, and Sony itself provides a means to unlock the phone's bootloader, and to compile AOSP for the device.
Of course, it fails in the "cheap" dimension, and also on "size" and "replaceable battery" ones. Still, as far as things that would be considered compact in the current smartphone market, it looks like close to the only option.
I recommended the Xperia Compact line to a coworker, and she says it's still too big. She wants it to fit comfortably on a woman's pocket. Something Motorola Razr-sized (about 20% smaller than the Xperia compact).
I can see that being a problem. Anyone that has tiny pockets and doesn't want to carry around a separate bag is mostly up a creek these days, even with phones that the market considers tiny.
You know they make a few slick Android flip-phones, right? The newest generation of the Samsung Galaxy Folder was announced a few weeks ago. LG also offers one, the Wine Smart.
Personally, I fit your description to a tee. My phone is a Samsung Convoy 2 (the 3 and 4 are inferior) from ~5 years ago. My camera is a small Canon EOS 1200D/Rebel T5. Even the cheapo 18-55mm kit lens that comes with the camera takes better pictures than an iPhone 7.
The cheap camera paired with a cheap prime lens (I paid $90 for a CEF 50mm f/1.8 STM lens) results in jaw-dropping clarity and dreamy depth of field blurs that no phone will ever match--until we overcome the physical limitations of current camera technology requiring light to shine onto a sensor.
The Convoy 2 packs a camera equivalent to an iPhone 3G. It gets the job done fine in daylight, and is passable in dark settings. The LED flash is almost excessively bright.
Personally, I have no problem carrying both with me. The only time I'm surprised by something I'd like to take a high-quality picture of is of another car I see while driving. So even if I had a 2016-level smart phone, the picture's still going to mostly be of a dirty windshield and my car's A-pillar. (Plus, you know, the whole dangerous and illegal caveats.)
They make much smaller cameras than mine that still take great pictures. I suppose someone out there really does drag around both devices with them. I'd expect that number to increase somewhat as mirror-less interchangeable lens tech continues to rapidly improve.
There seems to be an implication that the poster still wants to run apps with a moderately sized touch screen, which you can't do with a flip phone. Also, no one wants to carry around two devices.
Huh, how did you conclude that?! Also who exactly is the target audience for modern smart phones? How do you determine that and why are millions of users around the world treated like they're a single demographic with uniform wishes?
The target audience are people who aren't looking at replaceable batteries and upgradeable storage as deal breakers. Especially since there are better/popular alternatives for both i.e. powerbanks and wireless drives/internet. And the people who make that choice are the manufacturers who base their decisions on the general public i.e. product research.
So maybe you, the OP etc just need to understand that your requirements are niche and unlikely to ever be met in the more popular phones.
I ran with a flip phone for a while. I found the following downsides:
- No built-in mobile hotspot functionality, and no 4G/LTE
- No ability to use messaging systems other than SMS (Google Hangouts, Slack, etc.) except for maybe a few whitelisted ones
- No mobile maps
None of these would have been a dealbreaker 10 years ago, since no phones supported mobile hotspots or 4G or LTE, people either used SMS or some IM system that your phone did support (e.g., AIM - although AIM also had a pretty good SMS bridge, back in the day), and nobody expected you to have maps on your phone. Today all of those expectations are different.
It started life as a perfectly servicable Android phone. A little on the slow side, but not drastically so. The main problem was its 384MB of backing store. By 2015, very few Android apps supported installing to the SD card, and Google Play Services managed to eat almost all of the available storage.
Ideally, I'd like a modern phone with the same size and build quality of the Xperia Ray, the phone that fits unnoticably into my pocket and survived countless falls onto hard floors. I don't think it even needs to be super fast. Just with enough backing store to function as a modern Android device.
And knowing that such devices are possible is the reason I don't agree with the "you'd probably be fine with a feature phone" answer.
At the moment, I'm using a Z5 Compact. It's a great phone with solid build quality, but it's still too big IMO.