Sure, if you install a GNU stack (glibc, for example, being an important part) you can run typical Linux software on Android. It's not the default, however. While the Linux kernel has proliferated, the userlands are more varied; Android/Bionic on phones and tablets, uClibc on routers and other embedded roles, GNU/Linux for most servers and desktops--though even in that final category, we see substantial variation such as systemd versus init.

Sometimes this is to Linux's advantage; it underscores its flexibility, and the ability to use, for example, busybox uClibc on small systems is definitely an advantage. But other times, like having no standard UI toolkit that works across desktop, tablet, and phone, or having different approaches to managing services/daemons, the advantages are less clear.

Canonical was heading hard in this unified direction, but I'm not sure what their current phone/tablet plans are. Their stupidly implausible kickstarter seems to have disrupted these efforts.