What you describe already exists. I'm the founder of https://wundergraph.com and we're doing exactly what you describe, combining GraphQL with Auth and Caching, plus some more extras...
I totally agree. My startup uses graphql inside a lambda function. I'm not running at any scale yet but I just cant see the point of not leveraging all that autoscaling infra. Perhaps lambda at real scale costs more but I've not seen any data on that.