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.