AGGEMAM said:Note that all says that these weapons can be used to make trip attacks, and most even explain why they can be used to do it.
The special dropping the weapon to avoid counter-trips is just an added bonus.
Yes, I know.
All I'm saying is that the rules state certain weapons can be used to make trip attacks. This doesn't necessarily mean _other_ weapons can't be used to make trip attacks; the rules on tripping don't mention anything about particular weapons being needed.
I think the bits you quote just highlight that certain weapons get special benefits in this situation. You could use other weapons, but not get any such benefits.