A simple question has been raised. It seems that even though there are rishonim who allow pressure of various types for a man to give his wife a get - the Achronim require being very cautious because of the possibility the get was not given freely. In short they are choshesh that the pressure produced a get me'usa and thus is invalid.
What happens if the concerns are ignored. It apparently means at most that there is the possibility that the get is invalid but it is not certain. It also means that we are concerned at most with the possibility that someone might not want to marry the woman - but not that the children are in fact mamzerim. Thus if woman want to take the chance that they might lose a part of the population as possible husbands - what is wrong with allowing this to happen - especially she has a number of major rabbis advocating she do so?