That's where all the good record labels and record producers were. All good Canadian musicians/actors/directors go to the US. They largely leave Canada behind without much mention of Canada during their careers besides Drake and to a lesser extent Neil Young being the exception.
Leonard's first album had amazing production by american producer John Simon (who also worked with The Band, Simon & Garfunkel, Janis Joplin), probably the best in Cohen's entire career, so he chose well deciding to work out of Columbia's studio in NYC...
I'm struggling with the use of the word American here, both you and the parent posters. In my opinion all Canadians are just as much Americans as anyone from the USA.
Not sure what else you can call someone from USA, so I guess it makes a bit of sense.
I'd say Cohen is entirely Canadian. He has this very self-deprecating humor that you don't really get from Americans.