Aurora has a bunch of nice features WRT automatic failover, redundancy, and automatically scaling storage as you push more data into the DB.

Does Aurora do anything other than detect a heartbeat failure, shoot the node in the head and bring it up on another box WRT failover?

That is the basic idea on such things, though distributed protocols become complex when you have to consider split-brain, multiple concurrent failures, etc which all can occur in large-scale events.

Aurora leverages Amazon RDS Multi-AZ in this area. Their implementation has been battle-tested over many years and many many db instances.

I'm really wondering if something very close will be possible soon with AWS EFS.