We all know people can have nice words and hearts. That does not prevent them being indifferent to what they did to other peoples or their country did to other countries.
I do not want politicians to use tweeter so much. Neither to say kind words or hateful words. Tweets are not for serious work of solving society problems.
As for how Twitter should be used, it's a communication medium. People can use it however they seem fit. Would it seem more important if the message came via telegraph, telegram, telephone? History adapted to all of those as well. "Sighted ship, sunk same", "WAR", the Zimmerman Telegram, etc.
edit: I say this as someone who doesn't use twitter; it still seems like it has value, albeit small or insignificant at times
But thanks to the internet and platforms like Twitter, it may now be possible for a politician to reach millions of people without paying the Fox and CNN tax.