As has been mentioned, EBS can only be mounted to one instance at a time. If you could mount it to multiple it would effectively be the same thing, but then you have all sorts of write-locking issues.
As the rest of the comments also allude, a lot of the cloud-entrenched world has abandoned NFS, or at least in AWS circles.
I'm not one of these people. Rather than relying solely on puppet->all instances to handle multiple deploys, the convenience of an NFS instance was appealing, so essentially I have a relatively small (read: medium) instance that does nothing but manage the deployment filesystems and allow new in-security groups to connect. I have often though of abandoning this for doing deploys in a more "modern" way but I'm still not sure what the benefit would be other than eliminating a minor source of shame.
The analog here is running a MySQL or Postgres database in an instance prior to RDS. RDS provided enough benefit that the minor price difference in rolling your own no longer factored in. A more reliable, fault-tolerant and extensible file system is, like RDS, a huge upgrade. It may not be for everyone, but for some of us it's just another reason why AWS keeps making it hard to even look anywhere else.