I think you should file a support case on this. I tried to replicate this on a test app, and saw the same behavior.
When using the API, you can set the individual elements of an Address field - so I would have expected formula URLs to also be able to set the values of the individual elements in the same way.
I also tried to achieve the same results by using form rules to set the Service Address (in the child record) to the same values as the Billing Address (in the parent record) - but looks like the Service Address is not accessible to change via form rules. Again - I think this functionality should be there - to make Address fields more useful.
Let us know what you find out from Support!
