One way of looking at it, is Trump is a boorish fool, who should never have talked to another President that way, and who precipitated a war between Turkey and Syria.
Another way of looking at it, is Trump is a genius master of human psychology, and goaded Erdogan into an action which will ultimately destroy the Turkish Islamic State.
I'm leaning towards the latter.
I saw nothing unusual about the letter. Cut all the BS that diplomats talk.
Or, as demonstrated in the letter, Trump knew Erdogan had already committed to invade and the letter Trump included a letter Trump received from the Kurdish general Mazloum, who must also already have been aware of what the Turks were planning and contained unprecedented concessions to the Turks, which has not been released. It was a last ditch effort by Trump and Mazloum to deter, not goad, Erdogan. It is unclear if the Kurd concessions were a result of US pressure to appease Erdogan or if the offer was an idea of the Kurds and Trump merely decided to back the Kurdish carrot with the threat of the stick.
Trump did not need to goad Turkey into invading, Turkey had already decided to do so... the Kurds clearly knew it was coming and decided to offer an olive branch before Trump wrote the letter.