I honestly do not know why JMP chose to plot the variance instead of the standard error. The function from regression is a 'quadratic form.' They did not square the function. They chose not to transform it for the plot.
I don't think that the choice of standard error or variance makes any practical difference when using this plot to visually evaluate the performance of a design or to compare more than one candidate design. But remember that variance is additive, standard error is not. That property might give the use of variance an advantage.
JMP does not copy other software. JMP follows standards, but I am unaware of any standard for the FDS plot. Perhaps plotting the standard error is a convention in your experience, but I do not think that there is any convention either.
So what are you unable to do with the version of the FDS plot in JMP that uses variance?
You might suggest that JMP offers the option to plot either the variance or the standard error in the FDS Plot and Prediction Variance Profiler (Prediction SE Profiler, I guess) over in the JMP Wish List area of the JMP Community.