Plenty of options already exist. DynamoDB has both autoscaling and serverless modes. AWS also has managed Cassandra (runs on top of DynamoDB) which doesn't need instance management.

Azure has CosmosDB, GCP has Cloud Datastore/Firestore, and there are many DB vendors like Planetscale (mysql), CockroachDB (postgres), FaunaDB (custom document/relational) that have "serverless" options.