Tools that compile to CloudFormation templates offer a way to access (2) directly - to use alternative front-end syntaxes but to still deploy via the CloudFormation orchestration engine.
Tools like Pulumi (and Terraform) have their own deployment orchestration engines, which we believe offer many benefits - performance, secrets, components, transformations, aliases/refactoring, multi-cloud provisioning, and a lot more.
Cloud Control API lets us (and others like us) access (1) directly, without having to use (2) or (3), and thus being able to still offer the full set of benefits of provisioning via Pulumi, along with the full set of benefits of a well-defined AWS resource model.
Not something you can easily do with the declarative version.
Its something that you can do easily with the imperative API for CloudFormation plus the declarative description of the stacks in CloudFormation.