Mamzerus and marriage

A question was recently posed to me by a friend regarding the following situation: He got engaged to a woman, and both of them believed her to be a kosher yid. Last week her mother dropped a bomb shell that she did not have a get from her first marriage- thus making her daughter from this second marriage a mamzeret! The Beis din in the area is looking into the sitatuin but I have a question based on what I have just learned in Daf Yomi - Yevamos Daf 90. There they discuss that the Rabbis can annul the marriage by declaring the money used for kiddushin to be invalid and thus the marriage to be invalid- negating the need for a get. I was wondering why this is not used as a solution in cases such as this (where there are no children from the first marriage and thus no one is disadvantaged) and for agunot with husbands who refuse to give a get.

This is one of the major halachic questions of modern times. The Rabbis today do not want to rely only on annulling a marriage. If there are other halachic considerations to consider it may be possible to add this one as well. In a way it is a "too easy" solution to all marriage problems. It may be opening a Pandora's box. This is something that gedloei Yisroel willl have to decide on. If you want to read about it and get a better understanding, see: Professor Eliav Shochetman, Hafkaat Kidushin, Shanaton HAMishpat HAivrei, 5755 - 5757 p 307- 349; Rabbi Shlomo Riskin, Hafkaat Kidushin, solution for agunot, Techumin 22, 5752, p 191 - 210.