My favorite topic. Has President Trump changed our language? I like to watch 1930s movies to note how much the language, both word usage and pronunciation, has changed.
As you know, language is fluid and in a constant state of change. Some of the things that are considered acceptable nowadays cause me to cringe mightily. (Both in speech and the written word.)
As you yourself are saying, "has changed" and not has been changed (by anyone or even by Trump). I doubt that single persons even if they are presidents are that influential. If that were the case, then former presidents might also have made such an impact. Did they? IMO, it is rather the other way around: language changes bottom-up and not top-down. Trump is not exactly what is commonly understood by a smooth talker. He wants to come across as someone who speaks the same language as his following which is constitutive of an us vs them strategy that he's been pursuing. So he has adjusted his language accordingly or, alternatively, he happens to talk like that anyway. Leaving content and other aspects aside, what is striking is a range of vocabulary and a diction that reminds me of young people and which he uses frequently and repetitively. There's a simple sentence structure, on the one hand, and run-on sentences in his tweets, OTOH. He capitalises words in his tweets which come across shouty. He interrupts himself quite often and rephrases a sentence. He tends to use superlatives and adjectives like amazing, wonderful, great and repeats words like very, really, etc. for emphasis. He doesn't really switch codes and more or less sounds the same whatever the occasion is. It reminds me to some extent of Steve Jobs' key-note addresses to introduce the iPhone, iPad. Brilliantly presented, no doubt, but also taking a folksy approach deliberately using both simple language where required (You got, The problem is, We got, It's got) and syntax to reach the widest possible audience watching the pitch from all over the world. That's a successful strategy adopted by both of them. The wider and more heterogeneous the audience is, the less articulacy may be appreciated anyway. Trump's plain style is very likely to help him connect himself up to a given percentage of the voters because they use the same code. That's another reason why they like him. IOW, he doesn't influence them so much but they influence him.
I think what you are noticing Thomas is straight talk from someone who is not a phony career politician trying to impress who gets right to the point. You could call him a freelance talker who shoots from the hip with unprepared statements. He's not trying to impress. It resonates with most us.
Trump is a New Yorker and he reverts to type when addressing the public. I am certain he's a different man when making business deals. In speechifying I mean.