faster: "Still, I'd like to know why the verifier needs such a lengthy period of time connected to my computer, even long after I have done everything and verification has finished."....
I have a cable connection, and the verify sequence only takes a couple of seconds for me.
If your connection is remaining open after the sequence, you may have another issue.
I hate to bring up the obvious, but have you scanned your system recently?
Any system updates that need to be installed?

I'm eating crow because the game I had tried to install and verify actually was installed. It installed to Program Files which I never use for games. It even put an icon on the desktop, but I have so many they sometimes overlap.

I recommend eating almost any other burd.

Still, I'd like to know why the verifier needs such a lengthy period of time connected to my computer, even long after I have done everything and verification has finished.

With my apologies,
Holly B.