It's been speculated for a long time (presumably not only by me) that Barack Obama's speaking style – that of frequent and sometimes long pauses – was caused by trying to filter out all the classified information he has. The man was and is a pretty deliberate speaker – unlike Bush II who, when faced with this crushing burden of knowledge he cannot share or hint at, had a more conversational/Spooneristic style. Honestly, I wouldn't ever speak extemporaneously if I spent more than ten hours a day getting classified briefings on every topic imaginable. I think it's hard to explain how difficult that task is, and the pressure of knowing how high the costs are if you make a mistake.
And now we have an interesting experiment. We have a president who seems to only speak extemporaneously, and who also seems to ignore most classified briefings.
And sure enough, Trump's speaking style hasn't changed much. It was a complete mess to begin with, to be sure. He'd start a sentence five times before finishing it once. It is perhaps the most abortive speaking style I've ever heard. Even the insane homeless person who used to scream numbers at the lamppost near my first job out of college had a format, and seemed quite intent on completing all of his thoughts.
But Bush II and Obama are more interesting. Obama in particular – he's now speaking much quicker and obviously at least somewhat extemporaneously. Both Bush II and Obama were much quicker and more articulate on the campaign trail and in their previous jobs, but maybe the presidency just takes a lot out of you. Bush II has retreated from political life, it's hard to make statements about his speaking, as it's largely informal now. But from some comments I heard from him about his charitable work in Africa, he seems focused, organized, and clear. I strongly suspect the job doesn't have substantial mental wear and tear. They're just fine, now that they've been released from the burden of secret knowledge.
Of course, they could have, it seems, just spontaneously shared classified information like Trump does. That'd be a load off.