"Runway analysis" just tells you if you can stop, not how hot the brakes are going to get. "Maximum brake energy" is a LOT more than the energy required to get them hot enough to melt a fuse plug or trigger the overheat warning.
Indeed, braking too hard, too early will exacerbate the situation when the brakes or stopping distance is marginal. 747 Classic crews should realize that great care must be taken when more than Min Autobrakes are required.