What does “the bully pulpit has splintered” mean?

Bully pulpit refers to the position of power of a politician from which they exert their functions and authority. Because of technology communication nowadays is split over many different channels and the article suggests that this makes it harder for a politician to attract people's attention.

Bully pulpit:

• a position of authority or public visibility, especially a political office, from which one may express one's views. (Dictionary.com)

Origin:

• This term was coined by President Theodore Roosevelt, who referred to the White House as a "bully pulpit", by which he meant a terrific platform from which to advocate an agenda.

• Roosevelt used the word bully as an adjective meaning "superb" or "wonderful", a more common usage in his time than it is today. Another expression which survives from this era is "bully for you", synonymous with "good for you". (Wikipedia)

From World Wide Words:

• Half a dozen of us were with the President [Theodore Roosevelt] in his library. He was sitting at his desk reading to us his forthcoming Message. He had just finished reading a paragraph of a distinctly ethical character when he suddenly stopped, swung round in his swivel chair and said “I suppose my critics will call that preaching, but I have got such a bully pulpit!”
  • Lyman Abbott, in The Outlook, 27 Feb. 1909. Dr Abbott, a notable Protestant theologian and author, was editor-in-chief of the magazine. The anecdote was thought worth repeating in the New York Times on 6 March. Roosevelt was fond of bully as an adjective; when he returned to the US following his successful campaign in Cuba in 1898, he said “I’ve had a bully time and a bully fight!”