What are the benefits of "Restore Android ID from a backup" after a factory reset? As far as I can tell Titanium Backup is the only application that has the ability to restore this ID but there's no explanation of what it is or why one would restore it.

Without restoring I'm able to access the Play Store and restore apps and settings without issue and all the apps work fine.

Why should the Android ID be restored?
Some developers use the Android ID as a way of verifying who you are. So if you don't restore the Android ID, you will have to re-validate certain apps.

For example, Google Play Music and Netflix will see a new device tied to your account (source). Google Play Music limits the number of devices you can have attached, so people who wipe their phone multiple times to try out new roms may have problems trying to sync with Google Play Music as they reach the 10 device limit (source). You can deauthorize devices if you have reached your limit.

In practice, it's generally best to restore the ID if you are going to also restore apps via Titanium Backup. There is no upside to keeping a new ID, and there are potential downsides if you don't restore.