We did research on solving the DOS issue using static analysis at IBM (cf. https://arxiv.org/pdf/2009.05632.pdf). Our findings were that static analysis allows to determine (relatively strict) upper bounds on query complexity, which we assessed for two production GraphQL APIs (GitHub and Yelp). However, the static analysis requires some configuration to determine the (maximum) size of lists.

I was later involved in productising said research into an API gateway (called DataPower) offered by IBM. We implemented our GraphQL static analysis in a quite flexible and performant way (all of GraphQL's query validation and the static analysis are implemented in C++). The required configuration for the static analysis can be provided using GraphQL schema directives (cf. https://ibm.github.io/graphql-specs/cost-spec.html). Unfortunately, DataPower is quite inaccessible to the common developer.

I find that persisted queries are a very interesting approach to also solve this issue. They still grant developers the full flexibility to define queries during development, but then require providers to validate and vet queries only once before persisting them (instead of validating and vetting queries on every request). This has huge benefits for runtime performance, of course.