It would take much more than just a 'c' argument; one needs the colormap, the norm, and the values being mapped. Note also that the 'x' and 'y' coordinates of N points along the line require N-1 values for the colors of the line segments between the consecutive points.
I'm sure we don't want to overload the 'plot' function with all this. It might make sense to have a new function that would encapsulate the functionality shown in the example you cite.

*m sure we don't want to overload the 'plot' function with all this. It might make sense to have a new function that would encapsulate the functionality shown in the example you cite.

It is fine if that function is called from plot internally.

Functions in the matplotlib API should have a defined return object. plot returns a list of Line2D objects.
One could of course let it take a c argument (and all the other arguments needed) and let it return a list of differently colored lines. But that is highly inefficient; and we probably don't want to introduce such inefficient code.
Letting plot return a LineCollection would be a bad API; I think in general we try to avoid functions where the return type depends on some combination of input parameters.
Hence the only option is really to create a new method that creates and returns a LineCollection.

This was already discussed in #6040; I would suggest folding the two discussions together.

I'm closing this in favor of #6040. I don't think the discussion here to date adds anything new.