I actually think that unless your company is massive or has a lot of expertise in GraphQL already, using it for private APIs may not be the best idea, as it could be a sign of certain internal dysfunctions or communication problems within or between engineering teams.
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An example, however of the kind of filtering I was referring to, and why I still think it would be non trivial to do, even in something like ASP.NET, is the following: https://www.gatsbyjs.org/docs/graphql-reference/#filter. This of course isn't something you get out the box in GraphQL either, but the structure of the system made this (relatively) easy to do.
Of course you could add something like OData to your REST API which would definitely be a valid alternative, but that also would have its own warts, and is subject to similar criticisms as GQL.