I think I found some clarity from yet another stats textbook I got my hands on. From the text:

*"In fact, the chi-squared test of independence is equivalent to a test for equality of two population proportions. Section 7.2 presented a z test statistic for this, based on dividing the difference of sample proportions by its standard error ... The chi-squared statistic relates to this z statistic by **X*^2 = z^2."

*"For a 2x2 table, why should we ever do a z test if we can get the same result with chi-squared? An advantage of the z test is that it also applies with one-sided alternative hypotheses ... The direction of the effect is lost in squaring z and using **X*^2."

This last point is the one I was trying to ask about earlier when I mentioned that in doing a two-sample hypothesis test, we can actually specify a direction within the test itself. We can't do that with chi square. Thus, for example, if I wanted to know if women are MORE LIKELY to vote democrat than men (a one-tail or one-sided test), a two-sample z test helps me do this.

The textbook goes on to say that we need chi-squared for larger tables than 2x2, as we then have more than one comparison: "we could use a z statistic for each comparison, but not a single z statistic for the overall test of independence".