It's true that even an obsolete smart phone has lots of integrated features that you would be hard pressed to find or add to a micro-controller or tiny PC ( like the PI). There are even a few models that have some primitive IO capability, and lots of them at least have a serial port. So you can, with some effort, get some IO going.
But.
The huge advantage of the PI (and Arduino et al) is the development environment. It's free. It comes with the device. You can roll your own OS, drivers, libraries, programs and interfaces. Or build on the work of others via the community of developers who share their code. In other words, it's an open platform (yeah, yeah, quit nit picking).
A smart phone, on the other hand, is going to be much more difficult to develop for, unless you just want to make apps like everyone else. Many of those neat pieces of highly integrated hardware are not documented, proprietary, and don't give you the source code you need to made modifications. Yes, there's Android, but even there doing low-level things like single pin IO, or even just using the components to their full capabilities, is going to be hard, if not nearly impossible.
So for example if you want to make a robot controller, and you have an old iphone 3 lying around, and compare it to a Ras Pi. The Pi isn't going to have built-in screen, wifi, accelerometers, audio, battery and charger. But the Pi is going to be much easier to use for this application. The number of hoops you'd have to jump through to get the iphone working would make it a much harder prospect to use. By the time you finish getting, or custom making, the connectors/cables/circuits needed to hook it up, you'll have spent as much as a Pi or arduino costs. And that doesn't even address the development environment you'd need. Android phones have it much better off, but it's still not as easy as hooking up and programming a Pi or arduino.
Yes, you have a perfectly good cell phone that could, with some work, be used instead of a Pi. The problem is that the cell phone is going to take a lot more time and effort to hack than the Pi.