I think the central idea of the book is wrong. I don't think the use of reason has declined in the last few decades.
Things have certainly changed, and I can see why a "just the facts" person feels unfairly marginalized. Mastery of facts doesn't carry much weight.
Facts or Gore's reason have never been dominant in public discourse, except maybe for a "mini-Enlightenment" around the 1960s and 1970s. Dense policy proposals were kind of cool, because of basic respect for wonky, professional problem-solvers. But after major failures, the respect faded. Don't make the mistake of believing that wonky solutions ever carried the day because of reason. It was merely minor celebrity for the Reasoners.
Biases and mental filters have changed, and Gore failed to change with them. He became marginalized but doesn't understand why. He failed to adapt.
Ironically, reasoned study of how to move people has helped others adapt and defeat Gore. Better reason has allowed others to surpass Gore's ability to persuade. Only in the last few years, as he made a big movie, has he begun to catch up. It's not his reason that's attractive, it's his celebrity.
Public discussion has always relied on biases, mental shortcuts, and choices of trusted authorities. The supposed enemies of reason in Gore's book just learned better (using reason) how to become trusted authorities and win votes.
For a while, faith and similar badges of trust became more useful than an advanced degree and an erudite vocabulary. This too shall pass, and in fact its passing feels like a giant kidney stone in America's midsection right now.
What matters is finding ways to connect with people, to build relationships and trust, to get past biases and mental filters. Only then do ideas have power. Is that manipulation? No, it's just defeating the natural and pervasive skepticism that we all have against our own image of who are the purveyors of snake oil remedies.
We're all skeptics, and our biggest difference is what triggers our skepticism and makes us begin to ignore a public speaker. Professing faith turns off PZ Myers and professoring turns off a different set of people. And when turned off, listeners are deeply skeptical of whatever is said. What Gore decries is just the ability to use reason as a badge that inspires trust. People never understood and bought the arguments of Gore's reason, they just liked the people who sounded like Reasoners.