Can't hide the Home Screen in Adobe Indesign CC 2019

Since this is an option within a Panel, I would suggest trashing your InDesign Cache files (which is not the same as resetting preferences). Trashing Caches can fix missing options within Panels and dialogs.

To do so:

For Macintosh Users: The User Library folder in which InDesign’s cache files are stored is hidden by default on most Macintoshes. To access it make sure that InDesign is closed and click on the desktop to launch a Finder Window (Command-N).With this window in column view follow the path User>Home folder (it’s the folder with an icon that looks like a house—it may have the user’s name rather than “Home”) and click on the Home folder. With the Option Key pressed choose Library from the Finder Go Menu. “Library” will now appear within the Home folder. Within the Library folder find the “Caches” folder. Within the Caches folder find and delete the entire folder “Adobe InDesign”. I find that deleting the InDesign cache folder completely leads to a lasting change. 

For Windows Users: On Windows 7 and above the caches files are hidden. To find them go to the Control Panel and open Folder Options and then click the View tab. Then select “Show hidden files and folders” or “Show hidden files, folders or drive options” in Advanced Settings. Then delete (or rename) the folder at the end of this path: C:\Users\[User Name]\AppData\Local\Adobe\InDesign\Version [#]\<Language>\Cache.

It looks like you're not signed in to your Creative Cloud account. I'd start by signing in and then going back to that preference. It should be available. If it's still grayed out, I'd try resetting your preferences.

That still works for me in InDesign CC 2019 and macOS 10.14.

Try restoring your InDesign preferences and see if that helps:

Set preferences in Adobe InDesign