Bill,
Some of what I say might better be classified under "sanctified common sense" coupled with some biblical reasoning, but here it is.
The first question is, whether under the covenant-economy those connections were proper marriages at all. We could say something similar about an incestuous marriage--it may be a man an a woman (!), however, there is no possible way to legitimize what is in such a case an improper attempt at marriage union.
Second, the demands for purity under those redemptive-historical conditions appear to have been the consummate concern, overriding all other considerations.
That said, the point seems to be that these men were living two lives: one as an Israelite, the other as a heathen. And Ezra demands that they choose one.
A list of men are given. These are the men who chose their native God and people over the invitation of the heathen. They broke with the foreign women they had dallied with, even in some cases had children by.
There are at least two other scenarios that this list of names implies. The first is an unnamed list of those who left their ties to Judah, to Ezra and the Temple, and to Jehovah; and chose the women.
The other is an unnamed list of those men who may have sought a second possibility. Might they keep those women who, like Ruth, chose the God of Israel, and left their family and connections behind? The evident problem was that the foreign women, in the main, were drawing these Jews away from God, corrupting the holy nation by inducing heathenism into the tatters of national life. They were not leaving their families or way of life. The men drawn to them were weak of spirit, or failed to have the community in mind, or put God first as his servants.
This final option seems to me like a genuine possibility, but if it took place it must have been exceptional, like Ruth was exceptional.