1. Estimate the odds of successfully procreating upfront; Downside: Can seem boorish and unromantic and ruin the chance of a potentially successful relationship.
2. Keep getting to know each other and discuss once we're more comfortable with each other. If the answer is unfavorable:
a. Be honest about the reason for ending the relationship; Downside: Cruel to one's partner and heartbreaking
b. Fabricate an excuse for ending things; Downside: Dishonest and unfair to partner; guilt and heartbreak
c. Stay anyway; Downside: Reduces likelihood of having children
All this to say, I worry that your gut reaction may be filtering out the men most serious about having children. If someone knows you as a multi-dimensional being beyond a dating prospect first the approach changes. So I'd add this as a reason meet people through others means.
A lot of this makes sense. This seems consistent with my understanding of who you are. If your assessment of them was accurate, I'm surprised they left so readily. This makes me wonder what the 12 or so second dates would say.
I wonder if this suggests there were men you were even more interested in who you didn't go out with again because they seemed too perfect, because you felt you wouldn't be good enough.