It is how you use technology, and in that vein, how you teach your children to use it.
I find Twitter a fast way to get at authors that I read regularly, to reduce the advertising I would have to weed through scanning newspapers for good articles. I still read long-form articles and books, and have both an iPad and Kindle, but I typically use RSS an Twitter to scan titles and synopses for material to read. Can you see the value of scanning the top level before diving in, particularly with the profusion of material and sources?
As for the other values of Twitter, fun for the witty - brevity as the soul of wit - and diversity. You can come across others outside of your comfort zone, or wade into a lively round of repartee.
The number of people remembering entire books was likely very small, since literacy itself is a modern phenomenon. Progress really has made knowledge more accessible, and literacy greater. Rather than lament the loss of a few 'freaks' ability to remember texts, one can appreciate that no one needs to do that any longer, no longer needs to waste enormous time and energy to store a single source.
My father had several slide rules for his works with computers in the 50's and 60's, but one should realize how few people could do those kind of calculations, and how inaccessible higher math was to most people. Now almost all people can do the kind of calculations that at one time took an engineering degree.
This is progress.