As dsalo says, most libraries don't have the resources (both technical competency and time) to do any sort of custom programming, however minor. Also, many libraries depend on city IT for their IT infrastructure and may not have adequate access to their servers. Hosted solutions are becoming more popular but even then, you may have to get the vendor to agree to the catalog enhancements.
Our library does not use the Goodreads API directly, but we do get a link to its reviews via our Novelist Select subscription. We also have LibraryThing reviews. You can see an example of our OPAC layout here*. Currently, in order to see the Goodreads reviews, you have to scroll down past the "Copy/Holding information" section. In the future, I would like to separate them from the Novelist "suggestions" and move them up to be next to the LibraryThing reviews. Last time I checked, Novelist didn't have an easy way for me to do this but that was a while ago.
I love working with LibraryThing. That being said, I do have a slight preference for Goodreads reviews just because there are so many them.
*For those that are curious, our "professional reviews" and book jacket covers are from Syndetics. Novelist provides the series information as well as the content underneath the copy/holding information. LibraryThing provides, reviews, the similar items in the left column, tags, shelf browse, other editions, and Lexile ratings (where available).