I am not sure I understand what you want, but based on what I understood
the x scale seems to be the same, it is the y scale that is not the same, and that is because you specified scales ="free"
you can specify scales = "free_x" to only allow x to be free (in this case it is the same as pred has the same range by definition)
p <- ggplot(plot, aes(x = pred, y = value)) + geom_point(size = 2.5) + theme_bw()
p <- p + facet_wrap(~variable, scales = "free_x")
worked for me, see the picture
I think you were making it too difficult - I do seem to remember one time defining the limits based on a formula with min and max and if faceted I think it used only those values, but I can't find the code