While good for default configuration and reducing the total configuration the user needs to do, it's inconvenient requiring that all connectors on a cluster need to use the same converter. It's definitely a good idea to stay consistent, but occasionally you may need a special converters, e.g. one source of data happens to come in JSON despite you standardizing on Avro.
Note that these configs are connector-level in the sense that the entire connector should use a single converter type, but since converters are used by tasks the config needs to be automatically propagated to tasks.
This is effectively public API change as it is adding a built-in config for connectors/tasks, so this probably requires a KIP.