(Ok, I know there are real use cases for Docker, but I see a lot of hype as well. People telling my mathematician friend that she needs to use docker at the start of her project - it is likely to be a one off graph she needs to produce for a research paper).
Reproducibility is a big push.... but not like you are suggesting. Shipping a dockerfile is the equivalent of saying "This works, if you use this flask, this pipette, this GCMS and this piece of litmus paper"
Docker is not the only solution to problems. It solves some, but you can't tack it on to everything.
So shipping working code (even if it comes with a required pipette) might be a nice requirement for a peer reviewed publication to take on in order to keep their journal relevant. Shipping in Docker or similar guarantees reproducibility.
As you noted, reproducibility is a huge issue in the scientific community (according to docker users/vendors I've spoke to) to the extent that there are a number of funded startups trying to solve this problem (some using Docker.)
What has been also very surprising is the big companies who have read only copies of analytic data they want to run computations on - sandboxing the data scientists scripts in a container has helped them tremendously in terms of supporting the execution.