The blog post [1] provides additional insights that imply it can work well clients despite its ephemerality, and is optimized for client connection pools.
"Scaling operations are transparent to the connected clients and applications since existing connections and session state are transferred to the new nodes."
As for the public subnet concern, you can apply security groups to your database instance to ensure only authorized CIDR ranges can call it. Additionally, you can use IAM authentication [2] for DB callers (only recommended for light-weight applications with low concurrency),
[1] https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Using...