"It's the ultimate irresponsible medium. People I care about are readers... particularly serious readers and writers, these are my people. And we do not like to yak about ourselves."
"Irresponsible" is an odd word choice. From a structuralist perspective, I suppose we could say that a medium is 'responsible' or 'irresponsible' insofar as it causes people to act a certain way or according to certain norms. In this case, I think what Franzen is saying is that because Twitter is characterized by brevity, it discourages substantive reflection or discussion. This isn't necessarily true; you can make a point concisely. But even if we posit that there is a relationship between the length of a communication and its depth, I think it's safe to say that Twitter encourages reading. For many people, it works as a news feed curated by your communities of interest. Glancing at my feed just now, about two-thirds of the tweets posted in the past ten minutes include links to articles, some of which I will read, many of which I wouldn't have otherwise stumbled across, and one or two of which I might write about later.
In other words, even if people aren't having serious discussions on Twitter--which in some cases they are--they may be using Twitter to facilitate such discussions. In that case, it can't be considered an 'irresponsible' medium, even using Franzen's criteria. And although I appreciate his commitment to serious discourse, his criteria are, I think, overly rigid. If someone's using Twitter to convey simple factual information--"This thing is happening at this location at this time"--that may or may not be trivial (see, for example, Andy Carvin's work during the Arab Spring).
Incidentally, Twitter isn't a great place for yakking. People do sometimes use it to yak, but if that's all you do then people get annoyed. Beyond that, I don't know why Franzen has such a problem with yakking. People yak all the time and their yakking may be illuminating. What are the issues about which they repeatedly, idly, nervously yak? Do patterns of speech in their yakking point to some underlying feeling that they would struggle to consciously unearth? Sometimes the behavior of yakking is significant even if the content of the yaks is clearly trivial. If a person is yakking with you it may be a signaling mechanism: that they would like to move beyond yakking with you, perhaps, or that they are committed to participative social mores which encourage yakking in certain contexts. Franzen must know this because people yak in his books and sometimes he yaks himself.
For more on how to be a responsible Twitter user, see Megan Garber at The Atlantic.