With the latest release of Acrobat on 12th Jan (release notes), we have added this functionality, now when you close all PDFs, the Home view is closed by default. Please go to Help > Check for updates within the product to apply the latest patch.
More details here: What's new in Adobe Acrobat DC
Finally got some time here at work to look at this again.
As I understand it, closing the last PDF by hand also closes the Home view. Indeed, it does appear to work now on my test system, and I can even see the checkbox option in Preferences that controls it. However, it still appears that closing the last open document from a script does not close the Home view.
I'll do some more testing, but so far, scripting seems to still exhibit the same behavior as before. Is there, perhaps, a new app method that I can call from my script which closes the Home view (provided no other documents are currently open, of course)?