I don't think the OS is really the bottleneck here. I think getting a mobile device's hardware to run for this long is. There are a few things that make this difficult:
* Batteries - These currently only have so many cycles. A 10 year phone would need to provide a largish battery holding area allowing for two wires of varying voltages to be supplied. It would then in turn need to be able to charge at these various voltages through those two wires. I think voltages ranging from 1V to 24V would be a reasonable guess at where future battery tech would stay. Any person could then feasibly change their battery for some future tech.
* Connectivity - In just a few years, we've gone from only really having 2G to having just 3G/4G. In 10 years time, I think it wouldn't be unreasonable to think that maybe 4G will be switched off. I think it's unlikely that WiFi will remain for the next 10 years too. You need some robust connectivity module that hackers could connect to an arbitrary home-brew hacker's module. Something like UART/Serial/I2C/SPI.
Other things could burn out over time, but replacing those things becomes way too difficult. The processor, GPU, RAM, case, buttons and screen are just things I think that need to be the core phone.
Another place that could be interesting to explore is converting old, arbitrary phones into useful everyday devices. For example, I'm looking at converting my old HTC wild fire phone (the screen is small) into a permanent low-power alarm clock. It'll sit on the WiFi and if it sees my laptop/phone on the WiFi it will schedule the alarm, otherwise not.
I have another slightly newer phone with a larger display, so I was thinking or either making some notification board for my office or some very cheap VR headset for watching YouTube videos in bed without holding my phone up.
That said, there's no reason why all of these new "smart" devices couldn't reuse old technology. I think a small technology company that recycled old mobile devices into new smart devices would be pretty awesome. People pay loads for a recycled pencil for example, why not a recycled electronics device? On the far end of the scale I've seen some awesome coasters made from old motherboards.
I would love to see offices and schools buying more second hand kit too. There's no reason why thin client software can't run on an old mini-intel board, or even a semi-old smart phone. Kids don't need this year's laptops to write a report in Word. I think there's a big space for reuse here.