The left, in America at least, is pretty divided. We see it in things like the Women's March. This isn't to say the right has its own points of division but it is to a much shorter extent. Currently, the left is unified by one thing. Hate. Hate for Republicans, more specifically. This hate is an amazing unifying factor for the left. The only problem is that once Trump is gone, the hate will weaken. There most likely won't be another political candidate on the right as profound as Trump for a while. The point I'm trying to make is that hate is powerful, but it is only temporary. A Neo-Marxist acting as the left's "Jordan Peterson" might be just the thing to bring down the classic Liberals and unite the Democrats. This is an extremely interesting concept that the OP has brought up. I see people in the comments saying that a Jordan Peterson on the left would be bad because they don't want someone like that. I don't believe that's what the OP meant. A left Jordan Peterson would be, as OP said, a "coach". Someone to manage, or lead, the left's agenda through thick and thin. Almost like a face. For some context, I'm a capitalist(or as Marxists might say, a proletariat) and I firmly believe in a free market. The idea of a Jordan Peterson of the left is slightly scary, mainly because Peterson is someone many rally behind.