One of the claimed benefits of using a Write Through Cache is that its “really useful for applications which write and re-read the information quickly.” However, you can probably satisfy this requirement equally with Write Back Cache.
Instead I would think the unique advantage of Write Through is that the data is persistently stored in non-volatile storage (the database). So the data is recoverable if the system goes down, i.e. power loss. I think this should be have been stated as primary and unique advantage of Write Through.
The Write Back Cache is probably a better choice if quick data access is important and your not as concerned about data loss on power loss. In my experience Write Back Cache is commonly used, combined with an Intent Log. This provides protection against power-loss, plus the benefits of fast cache access.