Had it not been for the nexus between taxation and representation, I’m sure that the theories of representation would have received a more thorough airing. I would expect Northerners to advance the argument that, while women and children could not vote, they were part of the polity on whose behalf Congress was legislating. It would be very, very difficult to advance an argument that Congress was legislating on behalf of slaves.
Furthermore, as a practical matter, the inclusion of women and children in the basis of representation made very little difference, since the proportion of each was roughly the same throughout the country. The proportion of slaves by contrast varied a great deal.
But, these arguments must remain hypothetical. The fact is that there WAS a nexus between taxation and representation, and that shut down the argument. The ratio of 0.6 really did make sense for taxation, so it had to be carried over for representation.
As James Madison put it in the essay linked above,
It could not be reasonably expected, and that was pretty much the QED.