The Apple Engineers are aware of this issue and in theory are working on a fix to be released in a future OS update, but I felt compelled to find a solution myself just in case it doesn't happen in the near future, or is never truly addressed.
My theory is that when migrating a user from an older Mac there are essential user files missing that would normally be made upon the creation of a new user account. (At least on these new 2018 MacBook Pro's) So, after hours of testing, I found a non-destructive solution. You don't have to start from scratch, and you don't need to manually migrate everything one-by-one to a new user. Here is my solution:
Step 1: Make sure you have a backup of anything important
Step 2: Create a "New" user account
Step 3: Once logged in, copy the "New" user library folder into iCloud Drive/an External Drive (File Path: ~/Library/)
Step 4: Right click the "New" user library folder, click "Get Info", change the permissions of the folder so that your "Main" user is the owner or at least has Read/Write access.
Step 5: Login to your "Main" user account and make a copy/backup of the "Main" user library folder (If you have "Hey Siri" enabled, there will be a folder called "VoiceTrigger" that you will not be able to move. Disable "Hey Siri" until you're done to get around this.
Now this is where it gets a little tedious, but it is much faster than starting from scratch:
Step 6: Move the contents of the "Main" user library folder to the trash (Content within certain folders inside the user library folder will need to be dragged to the trash individually as the system requires certain folders to always exist)
Step 7: Move the contents of the "New" user library folder into the "Main" user library folder (If it asks, check the "Apply to All" box and click "Replace")
Step 8: Reboot
Finally, the Wallet & Apple Pay preference pane should appear in System Preferences. However, at this point you'll notice that all Preferences and App Data are set back to factory settings (Good thing you made a copy/backup of your original user library folder in Step 5)
Step 9: Select the contents of your copy/backup "Main" user library folder (this has all of your Preferences and App Data)
Step 10: Copy/Paste them into your current "Main" user library folder (File Path: ~/Library/)
Step 11: If it asks, check the "Apply to All" box and click "Replace" (Like in Step 6 you will have to move certain content from folders over individually)
Step 12: Reboot
At last, all your Preferences and App Data are back and you finally have access to Wallet & Apple Pay like you always should have!
This worked for me, so I hope it helps!
Best of luck to you all!
-Andy