vise grips and setting for a very tight grip when you go to close the vise grips to hold onto the tip. may work.
heating with a torch can help expand the metal of the tip. and help free things up.
you may want to try say BPblaster. (not wd40) but some sort of rust remover or like that is not flammable. and spray the tip a 2 to 3 times over the next couple days. letting things set between each spray.
i suppose you could always take a regular old hand held angle grinder. and do a little bit of grinding near the threads. to cause the metal around threads to become weaker the more you grind off. though might want a new tip on hand. to roughly gauge how much you can grind off, of the old tip.
being as dry and hard the dirt is here, mid summer can be a bad time to try and put in posts. and the dirt can be much like steel. and initially trying to get the drill bit on steel to stay were you want it. as tip of drill bit rolls around. same like thing can happen with a PHD.
i have seen a few old PHD, were the tip was just welded on. i have seen a few auger bits, themselves just be a solid piece of metal, all the way down to the bottom tip.
looking at
Model G20/40 | G2040 | PTO Auger | Danuser it does not seem like the point is can not be removed "may be wrong".
PTO Augers | Post Hole Diggers | Danuser on the larger size models for bigger tractors. it looks like the point on bottom of the bit are removable. due to them listing actual different points for sale.