- Makes caching more challenging since there are now more possible permutations of the data depending on what query the client uses. A hacker could just spam your server's memory with cache entries by crafting many variations of queries.
- Makes access control a lot more complicated, slower and error-prone since the query needs to be analyzed in order to determine which resources are involved in any specific query in order for the server to decide whether to allow or block access to a resource. It's not like in REST where the request tells you exactly and precisely what resource the client wants to access.
- Adds overhead on the server side. It requires additional resources to process a query rather than just fetching resources by ID or fetching simple lists of resources. A lot of work may need to happen behind the scenes to fulfill a query and GraphQL hides this from the developer; this can lead to inefficient queries being used. I have a similar complaint about database ORMs which generate complex queries behind the scenes; this makes it difficult to identify performance issues in the underlying queries (since these are often completely hidden from the developer). Hiding necessary complexity is not a good idea... Maybe worse than adding unnecessary complexity.