Indeed is a good idea, but Pi has a better power consumption rate.
Old mobile phones or laptops are riskier because of batteries. Some laptops can work without batteries as well, but do old phones?
If you can limit the battery to stay in the area between 40-60%, it'll last a very, very long time.
> but do old phones
they did, with modifications
I've yet to find a laptop mainboard that doesn't work without a battery. As I've written below, I'm getting extremely boring old office laptops with integrated graphics. Usually phones also work fine without a battery. However, I'm not touching phones because I will not fiddle with locked bootloaders and "the Android situation". Running plain Linux is a hard requirement for me.