According to DoubleAA, R' Shechter says that any three people have a right to declare items hefker through Hefker Beis Din Hefker.
According to that, why doesn't an average Beis Din have a power to mafkiya kiddushin lemafreya for a great need (like in a case of an Aguna)? Moreover, even when Rabbonim would permit aggunos to get remarried, I have never heard of them being mafkiya kiddushin retroactively even as a snif.
Let's leave aside the question of whether the concept of "kol demekadesh adaata derbanan hu demekadesh" (weddings are conditional on the agreement of the greater rabbinate) relies on their power to declare things ownerless.
700 years ago, the Rashba (Responsa 1162) asked why the rabbis didn't cancel weddings retroactively in the case of a happily-married husband who was lost at sea (and his wife lacks sufficient proof to remarry; this is known as the "classical agunah", "Type I agunah", or "naturally-occurring agunah.") He answers that the rabbinic power is only used in cases either where the whole wedding looked incredibly wrong (e.g. she was marching down the aisle when suddenly a different guy ran up and handed her a ring -- sorry, Hollywood!), or when it looked like there was a divorce ceremony but it was technically flawed. If the Torah says that marriage ends with death or divorce, it would be a grave overreach of the rabbis to end it otherwise, i.e. with "annulment", in cases where the marriage was valid and there was no divorce ceremony.
This is an extensive topic. Your suggestion is similar to that of Rabbi Riskin which was debated by both Rabbi Zalman Nechemia Goldberg and Rabbi Jeremy Wieder. The latter's opinion, which in many respects overlaps with the former, is summarized in this audio lecture and in his written rebuttal. The essential point he makes is that there is no precedent for retroactively uprooting a marriage without some form of divorce document, except when allowing a woman to return to her husband.
Actually, your assumption is not so true - A Bais Din CAN potentially invalidate a marriage, it is just not practiced today.
The underlying reason is pretty simple, if [most of] the Poskim see the Kiddushin as a mere monetary Kinyan (as opposed to some that claim Kinyan Issur or a mixture of both), then the rule that "הפקר בית דין" should surely work. So a Beis Din can invalidate the deal of Kinyan and therefore the whole Kiddushin.
A less viable option is to claim "כל דמקדש אדעתא דרבנן מקדש ואפקעינהו רבנן לקידושי מיניה" (Ketubos 3a) but this requires a consensus on what דרבנן means, usually, it does not mean "a specific BD" but "the general Halachic consensus". In that case, if the Kiddushin ceremony was truly Kosher there's no way to cancel it as everything went "אדעתא דרבנן" so we have to find a loophole in the ceremony (secular witnesses, drunk Rabbi, the ring purchased with a credit card, the bride was unconscious etc. :)
A more serious question is what BD can do that, and what empowers a particular BD to invalidate a marriage. As the marriage itself is not authorized by a BD (only 2 witnesses), so the husband can always say "I'm not subordinate to that BD at all.". Theoretically, only the High Sanhedrin or at least the Tribe's Sanhedrin can obligate a person which is nonexistent today.
Just think of it, you buy something in Texas and a week later get a letter from the Lubavitcher BD in NY that the sell is invalidated. Do you care?
My Personal NB: Interestingly, the Sages (though they could) did not obligate a couple to subordinate to a certain BD. In this case, we could use #1 and #2 more freely.
