"Most dialog is forgettable"-- and so is most personal history. And there's a good reason for this. There's simply a limit to how much data should be
If you were to write an about a dead person you knew, you wouldn't list every book they ever read or every committee they ever joined, nor would you write about the stuff lying around their house. To most compellingly portray a deceased person's life, you might write about specific, enjoyable experiences shared with them that illustrated how they made you or others feel, or the impact of work they did. Stray too far from that, and you're creating a laundry list of information no one cares about.
Three specific points:
1) Information Overload
The idea that increasing the amount of informational baggage attached to us will connect us to others in a more meaningful way is bogus-- that sort of information would be pretty useless for most people, and hugely beneficial for companies that aggregate data in order to generalize about human beings' behavioral patterns in order to better advertise. I doubt much of what Schell suggests is remotely intended to help people so much as market more effectively. His marketing strategy is effective, though-- excellent use of emotional appeal.
2) Pressure vs. Privacy
Another problem is that if we turn the things we monitor the things we would otherwise do privately, we increase the amount we are suggestible to others' expectations rather than our own and run the risk of being misjudged in the future. If information about what one reads, for example, is stored and available publicly, for the public to judge, for the very purpose of "getting people to improve their behavior" instead of reading that "romance" novel, then the things one feels obliged to read become public statements instead of private activities. If this increased amount of publicity were to be expanded far beyond books, as Schell suggests is beneficial, not only would we lose a significant amount of privacy to develop our own thoughts, but the types of ideas we digest and express could be influenced highly by advertisement, as advertisement can introduce and reinforce different social and political ideas. Again, this benefits advertisers more than individuals.
3) The nature of internet interaction/culture
Schell only spoke of the internet in terms of business-- online games, advertisements, etc. However, there is also a strong dynamic to the internet that isn't necessarily controlled-- the creative aspect of it. People will randomly do creative things without a credit to their name, and with a certain amount of (conditional) "anonymity," which can still reach a massive audience. A notable example of this is the Obama 1984 Ad, which created a lot of controversy and reached millions of people. Interestingly, the person who created it said in an interview they wished to remain anonymous for a while to avoid negative backlash in his social and professional life.
Schell would probably be in favor of nixing the "anonymous" aspect of the internet in favor of databasing peoples' online presence, in order to more "positively" influence peoples' behavior and look back upon in the future. The problem is, no one in 1 or 100 years should have all data they leave on the internet, anonymously or not, be held up as a weighty piece of evidence about what they are/were like (at least not with small, isolated pieces of evidence). For many, writing online is some form of learning experience that leaves plenty of room (especially for adolescents) for incredible errors in communication, logic, etc. Oftentimes after I post something on the internet, and especially on these blogs where there are a lot more new ideas flowing around, it's only a matter of hours, days, or weeks before my beliefs expressed in a comment change or are qualified. While online responsibility is important, there is the possibility this stored data would be used as 'sound bytes' that pigeon-hole people. Our student blogs have their own context-- much of it is about development.
If society were to adopt the "Schell Extreme" as the standard philosophy (I don't think it will), we might not end up improving our behavior so much as tailoring our thoughts to others' expectations-- censoring our own expression, in a way. With a desire to have a flawless 'image' or (preposterously suggested) 'family legacy' comes the risk of making people less willing to try out new ideas online or offline.