There is a huge network of people on the treifeh filth of Facebook who cheer on husbands who are broken and mangled and give a forced GET. I went onto Facebook and asked this question: The halacha is clear that a forced GET is invalid, see Rashbo in teshuva volume IV number forty. But you have decided that the Torah is wrong, and you want to permit a woman to remarry without a kosher GET. Such a woman has a child with her forced and invalid GET and her child is a mamzer. The child grows up, and is enrolled in a school where mamzerim are a problem. The child eventually will find out that he is a mamzer. Nothing can be done about it except to go to the Reform "Rabbis" who invent remarriage without a GET and who declare that the marriage disappeared, or that forcing a husband even murdering him is proper if he refuses a GET. But the vast majority of Jewish people are going in the other direction, becoming more and more frum.
Reb Yosef Shalom Elyashev died at the age of a hundred plus with a thousand progeny. A secular Israeli newspaper published this and guess what: Everybody knows it. Throughout the Torah or Jewish world, Orthodox children are flowing in great numbers, may it increase. But the secular Jew has a child and a dog. The child goes to Japan and marries a gentile lady, and the dog doesn't vote. The strongest element in Israel's army used to be the Communist Kibbutsniks, or similar such people. Today, the strongest pro-army element in Israel is the frumeh, although in some ways they are Modern Orthodox and may be strongly involved with the state, nonetheless, the future generals wear yarmulkas, and things are going to get much stronger in that direction. An Orthodox Israeli Colonel used to visit Washington DC regularly to discuss with the marines and the American soldiers various military techniques. When he refused to let a woman sing at some event there was an uproar. But he is the Colonel who went into Gaza and fought it out bullet for bullet, and he is the future, not the ladies singing.
As we get stronger and stronger and more charedi and more charedi, children from funny or forced Gittin are going to have more and more problems marrying if they are really Orthodox. And even to get a person with a mamzer problem a shidduch with somebody not so religious is hard, because if a mamzer has a child that child will also be a mamzer, and even a person who is right now not Orthodox, doesn't want to burn their bridges behind them and have a child that will disgrace the family and all he marries.
I once dealt with gedolei hador in Israel and America, including Reb Moshe Feinstein and Reb Shmuel Zalman Aurebach, about a questionable mamzer. I was heavily involved. I will just say this: Never in my life did I see a person with the yiras shomayim of the problem person, a doubtful mamzer. And anyone who takes a Jewish neshomo that can reach the top and make a mamzer out of them will not have to explain anything to me, but in a Higher World, they take these things very seriously. And all of those who participated in mamzer making will say their piece to the Mighty Angels of Accusing and Destruction, and let them educate these angels on the glories of making mamzerim.