I don't think it's too nostalgic to pine for longer, epic exhortation of ideas. People still give memorable speeches (cf. Obama's "More Perfect Union"), and people still memorize the speeches of old. They give context to the soundbites and give depth when we want to go beyond the misquotes. But yes, blaming twitter goes too far, because it certainly has its place, too. It's just another tool of communication that has its benefits and pitfalls.
We get moving speeches when issues hit so close to home that the words serve as kindling for our deeper emotions. Every speech is inextricably tied to its own context.
Malcolm X, "The Ballot or the Bullet" Ronald Reagan's Space Shuttle Challenger address LBJ, "We Shall Overcome" JFK, "Ich Bin Ein Berliner"
None of these speeches would have been as meaningful in a different time, with different events and feelings and happenings.