The share prices of the companies Trump has bashed have rebounded within the same day, so this is incredibly misleading to say.
Not that I disagree with the core point of your post.
For one thing, Obama's personal account (i.e. not @POTUS, but @BarackObama) explicitly says in its profile: "This account is run by Organizing for Action staff. Tweets from the President are signed -bo. [0]
No such disclaimer has been made about Trump's account, which tweets with the same characteristics and tone as it did well before his current presidential campaign [1]. You're right, though, that Trump's team does tweet for him on occasion. Either that, or Trump, who is famously not a computer user, has mastered the art of using two different mobile operating systems [2]
But the president of the United States speaks with the executive authority for an entire nation. It's questionable enough when a company's stock falls because Trump lashes out at them, and means it [0]. But what about the times he makes a typo, or just doesn't have all the info he needs at that moment when his emotions arise? Even asking that he types something to be sent through a Wordpress-powered system would give him the same megaphone, but adding a little more friction so that things that deserved to be trashed/called-out in his voice actually deserve so.
For those who say this amounts to making Trump less "real" of a man...sure. But he's no longer just a man, he's the chief executive of the world's greatest power. He gave up the privilege of "just sayin what I think" for the privilege of being able to unilaterally launch a nuclear war. Keep in mind that there are no checks and balances against this power -- it is utterly unilateral: http://blog.nuclearsecrecy.com/2016/11/18/the-president-and-...
Giving up frictionless communication in 140-character-sized comments seems like a reasonable thing to pass on, given the many extra responsibilities he has, and the extra weight each of his words have.
[0] http://www.nbcnews.com/politics/politics-news/trump-threaten...