Why are empty spaces around hippocampus and striatum not filled with astrocytes?
Short answer
Glial scarring is due to brain damage. Brain damage results in molecular signals to be released that attract glial cells. Spaces in the brain present during development are not characterized by signalling molecules associated with trauma.

Background
The key here is that glial scar formation follows damage to the brain, and is associated with healing processes in the brain, including those occurring after ischemic stroke (Huang et al., 2014) and physical trauma (source: Society for Neuroscience, 2010). Brain damage results in the release of inflammatory proteins that signal glia to form scar tissue (e.g. Patel et al (2013)).

There are many vacant spaces in the brain (Fig. 1), most notably the four ventricles. These spaces are there from birth, and are actually formed within the first few weeks after conception. Because there are no signals involved from brain trauma, and these structures should be there, the glial system does not get signals to invade these areas and fill them up with glial scar tissue.

Also note that glial cells have little to do with neurogeneration; glia is not nervous tissue.  


Fig. 1. Brain ventricles. source: Anatomy Note

References
- Huanget al., Int J Med Sci (2014); 11(4): 344–8
- Patel el al., Int J Physiol Pathophysiol Pharmacol (2013); 5(2): 73–90