Seems like persistent subscriptions aim to solve two problems:
Server-side checkpointing for use cases when events are being forwarded to a place that doesn't have the ability to store checkpoints (message brokers), or users just don't want to deal with checkpoints.
High availability of subscribers (consumers)
Each of those cases can be solved separately. It might be a good idea to allow HA for consumers using the Connector, and also use server-side checkpointing provided by Connector.