Hey all.
This is not really a question, as I know the official answer if it was a question:
Q. Can we use AWS EFS as backing for the shared home in a BitBucket Data Center installation
A. No, it's not performant enough.
I understand that EFS is not considered performant enough for workloads such as git. This is due to the nature of git, in that it typically makes many small writes/reads and that EFS has increased per-operation latency due to its distributed nature. It's well documented that EFS is a little lacking in this area compared to more conventional NFS shares. This is despite the continuous improvements AWS make to the service.
I imagine that in larger installs, this may well become a serious problem.
However, I would like to discuss the feasibility of using EFS in smaller BitBucket instances, especially when using EKS, as it seems a natural fit for this purpose, especially if it is sufficient for your particular scenario.
I have just finished a batch of performance tests on our proof of concept instance of BitBucket on EKS, imitating heavy use scenarios that we would not typically see in our production environment.
My finding was that, for our use case and instance size, EFS is easily performant enough for our requirements.
To put a little more context into what I mean by a small instance size, when I look at the BitBucket instance size here (https://confluence.atlassian.com/enterprise/bitbucket-data-center-load-profiles-962360410.html) ours comes out at about 1/10 the size of a 'Small' in all the below metrics.

To measure the performance, I simulated multiple concurrent git clones of our largest repos and was easily able to achieve higher overall sustained throughput with EFS than we ever see on our production instance. This was on repos with many small objects as well as repos with larger objects.
So I guess I do have a question.
Is the reason for not supporting EFS purely based on performance? This would make sense for Xlarge, Large, Medium and maybe even Small instances. But on something 1/10 the size of that (Could we call it XSmall? Micro?), would it be acceptable to use?
Are there other non-performance based reasons to not use EFS for the shared home on BitBucket? Could it break anything other than performance?
The support issue.
If we were to go ahead and use EFS for this, we do understand that it's not officially supported. If we had any performance issues, we could not raise a ticket for them.
On the flip side, in the worst case it would not be terribly difficult to migrate the data stores off of EFS and onto some more performant disk such as EBS. We could do this if we really needed support (Of course, I am talking about after the Helm Charts are officially supported).
Any thoughts on this subject? We would like to proceed in this direction. It would seem inefficient for us to provision some extra clustered NFS service for no tangible benefit, when EFS is sitting there waiting for us 
Thanks for reading my essay!
Tom...