It's tough enuff to straighten fork tubes in a press with jigs and fixtures. When you view forktube assemblies on the bike, you see dual support from the trees at top, and tubular reinforcing from the sliders at the bottom.
So, when fork tubes get bent, they tend to bend in a 'V', in that short unsupported zone between the bottom triple and slider top.
Setups for straightening in the press normally confine all forces between those two endpoints, the bottom triple and the slider top, about 5"-8" worth of fork tube between the supports. Hence the need for a stout press, and focusing the press forces to the peak of that 'V', leaving the normally-still-straight ends out of the picture.
Trying to press out that 'V' with the fork tube supported at the ends usually results in a squashed 'W' shape, and the tube may bind in the lowers...