Only later I found out about that, when using a value of saved for default, I could boot on whatever system I had last booted on. However, since I had once read that it was not possible to select the boot OS from the OS itself, I didn't check that it was actually impossible until much later.

And it turns out it is possible and easy. You just have to invoke the grub-set-default command. Since it was still necessary to invoke a command and to know the index of the OS to boot, I decided to code a small shell script. The script, which can be configured from a few environment variables at the top of the file, will auto-detect the installed OSes (and which one is the current default), show you a list where you can select which one to boot and then invoke your preferred session manager to proceed to logout (you'll have to set it by yourself if you don't use Xfce).

You can download the script here: grub-reboot-selector.sh.

Note: this script depends on Zenity and a flavour of sudo (gksudo and sudo are currently automatically detected).