Sounds like the academic community should be charged for access to the data, if there is so much value in there.

The media is clearly benefiting, with many stories backed by a Donald Trump tweet. But if the tweets weren't free to begin with, they might not be as newsworthy.

> the media is clearly benefiting

Journalists certainly are. Getting quotes was hard work. Now it consists of trawling Twitter. Not sure if this has been a boon or bane for journalism, however.

> Journalists certainly are

In the short term, anyway. The substitution of Twitter-trawling for actual journalism and research is doing immense damage in the long run.

For full access to the twitter archive, they are, though a lot of data can be gleaned from what's publicly posted.

In retrospect I should have assumed that to be the case

I think you (and many others) have this relationship by the wrong end. Things which are valuable are frequently rare/unique, whereas there are many unique/rare things with no value whatsoever. As others in this thread have implied, the lack of ability to monetize is strongly correlated with a lack of real value.