As far as I understood, support libraries may work as alternative of built-in APIs, but they are not supposed to be, because they directly effect the size of the application.
For example, a support library is of 2MB, and to use its functionality, it takes all classes, resources, etc (of 2MB), so now classes.dex (Dalvik executable file of all classes being used in application) of my application also include that support library classes, and same for resources. So, if without support library my app size was 1MB, then now with support library the size is 2MB extra, which means 3MB total.
Now, suppose this support library feature is so common that on single device, if I have 10 apps, then at least 9 are using this same support library, so 9*2 = 18MB on my device is being used by the same support library, which is repeated in every application, which is bad, because for now 18MB might not be so much, but the space required can increase, if you have more applications using that support library.
Thus, the best option is to have that 2MB support library already in your OS for any number of apps, instead of having it for each application. So, support libraries are meant to be used when you really want some efficient features in your app to support older versions.
Another question arise here:
why not this support library is added to the OS as its own update, so that every app without size problems can access that functionality?
The answer is that there could be a lot of errors. Suppose some user doesn’t have that update (support library) installed…
There is also the chance that as an update, it may not work as efficient as supposed to be, or may cause problems while integrating with the OS, as we already seen that each OS (windows, Linux, mac) comes with new versions, instead of just giving updates for life time for all new features.