Besides my database servers, all of my machines are ephemeral[1]. I can lose machines and spin up new ones automatically (and therefore scale elastically).
EBS adds an unnecessary additional point of failure that I want to avoid at all costs.
Having run production systems in EC2 since 2010, I've survived numerous EBS outages as other services have crashed and burned by sticking to this philosophy.
[1]: I don't use EBS for my database servers either. I use a replicated DB that can lose multiple machines simultaneously without loss of data (and is backed up to S3 in case of a catastrophic event).