It should be obvious to all as to why in our history it became halachically crucial to rule that a Jewish child is born to a Jewish mother, the mother’s jewishness alone is the concluding factor. End of.
Of course there are complications in marrying a person with a non Jewish parent, those complexities are no doubt best judged on their individual circumstances. To those that wish to bring in different arguments from various Gadolim, do so if you wish to intellectualise the discussion in theory, BUT in practicse halacha is clear and simple on this. Jewish mother = Jewish child, a state of affairs given extra impetus by the Shoah.
Sure there are many who would not want added complications when contemplating marriage partners and also those that seek the value of yichus mispacha, but most important of all is the bond and chemistry between the couple. I have seen marriages arranged by eager parents on the basis of yichus and communal prestige, not always a recipe for married bliss!