What is value and use case for Deep Learning AMI (DLAMI)?

The value of the DLAMI (https://docs.aws.amazon.com/dlami/latest/devguide/what-is-dlami.html) is ease of use and saving time to get up to speed in a development environment. If you are developing code for ML there is a huge variety of frameworks and software that you might need to install. The DLAMI includes the more popular ones, so you may quickly deploy a machine complete with common dependencies. This results in a reduction of the time needed for installing and configuring things. It speeds up experimentation and evaluation. If you want to try a new framework, it is already there.

The second reason is that AWS keeps the AMI up to date, so you may just deploy a new AMI periodically rather than having to patch. Again, this saves you time and lets you concentrate on the underlying development and business activities.

All that said, for running in production and at volume you might want to use a different tool, I would imagine that for most cases creating docker images to your specific requirements would make a lot of sense. No need to go over the good and bad points of containers here.