This is one of the limitations of OOB Address entity., not being able to create N:1 relationship to other entities (case in this scenario). It is not possible to directly associate case with address using OOB configuration.
Here is a workaround
1. Store 'Address type' when creating addresses for account
2. On Case, create a similar (AddressType) field say 'Service Requested at' and then the user can select if it was home/office/other address types.
This way user will know where the work was done for a customer's case. This will require a bit of user training but is better than going for a custom entity for address.
Optional: If you want to see that address on the case form then you can do so using a script/plugin and copying the address based on the selected address type on case.
If my response helps you in finding your answer then please click 'Mark as Answer' and 'Vote as Helpful'