”Only values that arise from within the halakhic system play a role in producing pesak.”  I agree completely.  Traditional poskim are careful to frame a pesak that way and that is what legitimately constrains the range of possible pesakim. However, as is self-evident, more than one halakhic path forward may exist. The question is what points a posek one way versus another? That is a meta-halakhic question and probably a psychological or sociological one as well. Asserting that only Torah influences are legitimate in forming a posek’s orientation is the what is argued. I have not seen any arguments that would support the position restricting legitimate influences only to those that are Torah based.  In any case, many/most poskim may not necessarily be sufficiently self-aware.  Something as simple as one’s empathy for a situation is IMHO the result of various influences; for example, awareness or evaluation of a situation’s consequences, clearly not in the main derivable from Torah sources is clearly a legitimate basis for differing poskim‘s differing orientations.

However, what we are now witnessing is far worse. Those with a disdain for anything but learning Torah as practiced by say Rav Shach ztl, end up incapable of being a leader and posek. They may be living an ideal existence, but not one that prepares them to opine on the issues of the day. The Sanhedrin did not learn 70 languages from learning Torah. The Metonic relation which hazal adopted is nowhere in the Torah, (thank God, it is faulty) nor is the average lunation (almost but not quite exact and more critical) nor the relationship between stars and darkness. Shmuel did not become a baki be’shivielai de’rakiah by studying Torah. Rabbis without such knowledge did not attempt to create calendars.

There were many great poskim, RMF ztl and especially RSZA ztl for example, who worked diligently to acquire secular knowledge to pasken; today there are defenders for those who do not. That I find problematic.