The halacha does not come sbout merely because of personal authority and say-so, but rather because someone with sufficient personal authority invokes such to declare a reason for a given halacha (assuming that no one of requisite stature and position argues with him). Your objection seems to be the lack of a teshuvah stating the specific reason for the invocation of the personal authority of The Gedolim, but if the reason exists, the lack of a teshuvah is not so much an impediment to the legitimacy of the gezeirah as it is a source of frustration to those who would like to learn the sugya b'iyyun (The gezeirah against g'vinas akum as discussed in the Mishnah comes to mind as an example of a similar case, despite its difference in that it involves a real Sanhedrin).One could theoretically posit that the reason is insufficient to enact the gezeirah in question and The Gedolim either are mistaken in their reasoning or are overstepping the bounds of their capabilities within the halachic system (for reasons proper or improper), but I would not place those words in someone's mouth without asking for prior clarification.
It seems to me this raises a new interesting point (and I hope I am not misinterpreting Josh!). If someone formulates a halachic position based on sources, proof, and reasoning (whether that reasoning is revealed to the public or not), is that final psak justified by virtue of the authority of the person who arrived at the conclusion ("someone with sufficient personal authority invokes such to declare a reason" as Josh put it), or does the reasoning constitute its own justification? I would suggest drawing an analogy to the Supreme Court ruling on an issue of constitutional law – is the ruling binding because of the authority of the constitution, or because of the authority of the court which has interpreted the constitution in a certain fashion? Isn’t that issue at the heart of the question of originalism? (I am not a constitutional lawyer, and have been meaning to read this book but have not had time, so my analogy may be off). To take the extreme opposite position as Josh, one could argue that halachic conclusions are no more a function of the authority of a posek any more than the law of gravity is a function of the authority of Newton who discovered it.
R’ Tzadok haKohen (Tzidkas haTzadik #90) writes that the Torah, nefoshos of Klal Yisrael, and the physical world are parallel entities; all three are in flux, and the only constant is their relative connection to each other. We believe halacha is eternal truth, but what that eternal truth says is relative to our context of interpretation. In that respect, halacha is very different than a scientific law which is true at all times and places independent of the observer (yes, modern philosophy of science would reject my distinction, but I don't want to debate science now). But does the fact that there is no one eternal fixed standard of truth in all times and places mean we need to invoke the authority of the posek to validate an interpretation, or does the interpretation validate itself relative to the context in which it is presented?
I will add one caveat, and that is if we had a working Sanhedrin which did have a license to legislate, Josh’s approach fits perfectly (and Bill Selliger has hit on this in his comments as well). Legislation can occur behind closed doors (at least in halacha) with the public not given full access to the debate and reasoning behind a law - an enactment is binding simply by virtue of Sanhedrin legislating it into being. But we have no legislative body in halacha anymore, no Congress that exists to enact laws, only a "judicial branch" of ongoing interpretation. We can differ as to how much of an “activist” halachic court we are willing to tolerate, but ultimately, the system of psak and interpretation demands fidelity to the constraints of existing halacha without allowances to simply make new provisions up out of the blue.
Does that mean that Rabbinical authorities cannot implement public policy initiatives above and beyond halacha? Obviously, they can! But in doing so they step out of their roles of formal interpreters of law and into new roles as social and political activists. Does or should that make a difference? Lets leave that one for another time : )