This falls as a more-involved way for Twitter as a cooperation to support academic research on its platform (rather than just extending API limits for .edu emails etc..) but one avenue for very supportive, engaged involvement would be curation and publication of topics.
That is to say, imagine Twitter itself publishes corpora of tweet IDs corresponding to major events like natural disasters, political events, etc... This creates a streamlined way for those studying the social dynamics surrounding major events to implement real-time study of ongoing events, and broaden the scope of existing analyses.
Currently, the study of past events relies on hydrating tweet IDs from previous major events all compiled by data-horders and college librarians and archivists. And because of the non-trivial steps involved in accessing the data, to my knowledge there are only about 15-20 examples of 'high quality' datasets which would be suitable for use in any major, longitudinal study. Twitter leading the way in publishing these events would serve not only as a long-term marker in history, but as a reference for researchers the world over.
There are certainly individuals out there who would rather compile their own topics-- this is a rich research area in itself-- however there are many disciplines where the current barrier to entry for studying the twitter discourse around an event is prohibitively high. A Twitter-curated list of Tweet IDs surrounding an event (perhaps compiled based on keywords, location, and networks properties?) could be shared as a de-facto resource in the Online Social Network field.
It would represent a significant effort on Twitter's part to actively maintain and curate these databases. However it would go beyond what any other social media site has ever done in terms of supporting academic research.