The performance of EBS is pretty bad, and getting decent performance is expensive. Having said that, if your application runs in memory and disk usage is infrequent then it is probably fine to use EBS. EBS is also much more expensive than the instance storage, but it is also durable unlike instance storage.

On the whole, "never ever EBS" is too strong language making it incorrect. As usual, it depends.

TLDR: it's okay for backups, but in critical path it's a world of sadness. Failure modes are too painful.