While it's true that deployment exceptions are not a public API when developing with the CDI programming model, they are a public API for tools and in testing environments. It would be useful to standardize the deployment-related error and exception classes so that these tools don't have to rely on classes from the implementation.
One example occurs in the CDI-TCK and it's counterpart, Arquillian. A test may want to verify that the code will result in a deployment error. Currently, to detect this exception, it's necessary to rely on an implementation specific exception class, which makes the test non-portable.
Another example is a tool that starts a CDI runtime or server that provides CDI. The tool has to check for the implementation-specific exception to know if the deployment error is caused by CDI (and to capture and report that error). It's important both when CDI is used for standalone bootstrap and for a container that provides CDI.
javax.enterprise.inject.DeploymentException extends RuntimeException