I've been looking into getting a Raspberry Pi, but I end up needing a case, a display, and some way to power it, and wanting some degree of portability. It seems to me that even the most outdated cellphone has far superior features (screen, touch screen, Wifi, 3g/4g camera(s), battery etc) in a much better form factor. The only thing that is missing are the digital/analog in/out pins. So why not flip it around and make a USB or bluetooth peripheral board with just the pins?
If you have a phone that can run a full Open Source OS, with full access to the hardware, then perhaps you indeed have a better solution than what a Raspberry Pi can offer. Note that people have taken the processor from modern phones and turned it into a Raspberry-like board already (See the Odroid board at www.hardkernel.com). However, most phones do not cost $35 (not without a wireless contract at least) and do not have GPIO, I2C, UART and other pins openly accessible. The Raspberry Pi is geared towards people who look for an easy to use, open, programmable environment for learning all about computers and electronics, and also attracts hobbyists and professionals who like the standarized format and broad support this board gives. But it is only one of many possible solutions. Odroid, Arduino, microcontrollers - all have their own use cases and audiences.
I think this depends on what it is you are interested in doing. As Phil B. points out, the pi has a lot of things that a phone does not,1 and as you point out, a phone has a lot of things a pi does not. They are two different things ("apples and oranges"). While there are cars that are also boats, most people who have cars and want boats want the boat separately. Of course, if someone came up with the perfect car-boat, that might change, but do not hold your breath -- it may be a very misguided concept.
So why not flip it around and make a USB or bluetooth peripheral board with just the pins?
You would not have the same potential with that -- the pi GPIO pins are processor pins. They are the kind of thing that is used to implement a bus (such as USB) from the processor to a peripheral. You could simulate the concept with a peripheral on the other side of a bus, but it is hard to see who would want to use such a thing and for what.
Keep in mind the pi is not a piece of consumer electronics. Although it is used as a media player, I think if that kind of thing is your primary interest, then other than being really really cheap it does not have much going for it. Put another way, if you are looking at it in terms of the kind of things you would do with a smartphone, it is not for you -- you will only end up disappointed and frustrated.
1. A pi has things even a $3000 desktop does not have. You cannot really access the I2C bus, etc., on a normal computer. This is why it is called a development board.
I use both old Android phones and Raspberry Pis. Each has strengths that the other cannot easily reproduce.
An Android phone is fine if you're comfortable with developing Android apps and being limited to the features you have access to. On a rooted phone, you should have access to most features. The phones have an impressive array of sensors (light, compass, GPS, more), a built-in battery/UPS, outstanding cameras and wifi. If you want these features in a handy, self-contained package, a smartphone is hard to beat. I can buy a Droid Bionic for roughly $65 used, and use them as remote network cameras, polled by my Linux server running motion.
The RPi lets me run mainstream Linux programs such as Node and Flask for server development. They provide a cheap platform that I can use for open source development using a bewildering array of languages and pre-built, free libraries at no cost. Programs written for the RPi can typically be run on a full desktop and vice-versa (within the limitations of hardware). I can also use the array of powerful open source software tools that previously required me to haul around a couple of laptops in a convenient form factor. I have used the camera module, but it pales compared to the smartphones for quality (though it's certainly useful for other purposes). It has no battery, but I can plug it into a 10,000 mAh battery for hours of use when needed. I don't do hardware development, but even without the GPIO capabilities, the RPi is irreplaceable for me. The RPi can be plugged into a wired network, or configured as an access point or wireless monitor. I can plug the RPi into a monitor and use a USB keyboard and mouse for comfort. I can plug 8 USB-serial adapters into a hub and use it as a serial terminal for configuring network equipment. I use RPis for network testing. My typical RPi costs about $85 (RPi, case, power adapter, 2 USB wifi adapters).
So while you could, conceivably, make one to much of what the other does, there's no real reason to do so. They won't do it as well, and you'll have to make compromises. They are different beasts. They compliment each other in many ways (phone makes good user interface to wifi-connected RPi). It's not a zero-sum game. You can use both.