"often people put forth the argument that the TP>OP with absolutely zero evidence to back it up."
1/ Both sexes can use it.
2/ Only wielders of the TP can sense other TP users.
3/ TP can do things that are IMPOSSIBLE with the OP (see Grandael).
4/ Foxhead medallion is very unlikely to work on it.
1-3 means TP > OP.
The ambush possibilities of wielding the TP alone makes it the superior choice.
Foxhead is created by using the OP and the TP is a lot different than the OP.
These ter'angreal do not appear to be extremely rare, since both Cadsuane and Nyaneve have one, and since the TP was very rarely used in AoL likely nobody bothered with a defense. How could a defense be build for something the Light forces have no idea wtf it is? Not like they could examine the TP. I would think all or at least the large majority of these ter'angreal were created to protect against mad One Power male AS.
Possibility: Shai'tan can increase the amount of TP on receives beyond OP strength limits. We know he lets Grandael wield almost nothing, while Moridin can wield massive amounts.
Sorry Entreri but the RJ quotes show there are more than enough drawbacks with TP to offset any advantage.
As for the foxhead all you offer is a good deal of speculation(including how often DF's used the TP in the AoL), although it would seem a huge stretch to say the forces of the light did not know what it was during the WoP. Bottom line with the truly do not know either way if it would stop the TP...
Only drawback is 'rapid' death, which is a HUGE drawback, but as said by RJ: "And eventually, unless you are given immortality by the Dark One, you are dead. "
TP > OP as a fighting tool, as clearly anyone can see. TP is Shai'tan's Power.
Forsaken are immortal and we know that Ishamael has been brought back and Moridin said "Death holds no fear for him", which implies he will be indefinitely brought back as long as the Shai'tan is "free".
One only needs to ask Brandon to be certain if the foxhead can stop the TP. Given what I described, very very unlikely to stop the TP.
Male channelers can't see weaves of Saidar, does that mean they can't fight women? The answer is, of course, no. So it not being visible isn't a very useful property, particularly against Nyn, who wouldn't be able to see saidin either.
4 is... unlikely, and your explanation flawed. LTT in Rand's head knew exactly what the TP was, as was made clear by his reaction to it. I have little doubt that it was used often in the War of Power, esp considering it was used to make trollocs and the like.
And death isn't the only drawback, addiction, and insanity are there as well.
Neither can the women see the men. Thus, there is no advantage.
Now wielding the TP a male can certainly "see" saidin (Watcher, book 7). Thus, Ishamael would have a large advantage over any saidin user.
The greatest advantage in combat is surprise.
As for seeing saidar while a male is wielding the TP, probably unlikely but I would not completely rule it out. It is the Power of Shai'tan.
Yes, LTT knew what it was, but according to the Forsaken it was only used in very dire need. LTT of course had many encounters with the Forsaken and especially Ishamael.
How do you make a defense against something, when you don't know the specifics of it and cannot test your ter'angreal?
Where does it say that Aginor used the TP to make the Trollocs? Using the TP for that long in order to create the Trollocs would be likely lethal.
Once given immortality, in battle the TP rules supreme.