The main issue with that right now seems to be the lack of real incentives: those badges are nice to have, but in the end you're evaluated by publications in highly regarded journals and conferences, citations, and funding brought in. Those things of course tend to let people focus on novel, fancy, exciting work, instead of the time-consuming process of making things easy to replicate by others, or even replication of other people's experiments. Incentive-wise, the publication business follows the principle of fire-and-forget.
What's needed, but I believe very difficult to introduce, is the strict expectation of independent replication. That would mean replication as part of the core review process, which would A. create a lot of work for reviewers B. initially reduce the attractiveness of whichever conference introduces it first.
One thing that would be easy to introduce in computer science would be to make it mandatory to share all code used in experiments - if you cannot/won't do that, you should not able to take part in this game.