There is no question of the correctness of your statement above. But to pretend that after 25 to 30 years of a "happy" marriage, if the guy suddenly runs off with his secretary, we discover he never had the intention of having children (despite six kids) - that is quite a stretch - who is kidding whom. The need is for some honesty.
Well that wouldn’t be a valid reason for annulment, and I doubt that would be the factor in granting an annulment. It would certainly be a factor if a couple were childless due to one spouse’s refusal to procreate after pledging to do so (if possible) during the wedding. If someone has six kids, it can only be assumed they intended to have children when they married.
Psychological immaturity is, from what I understand, a big factor in annulments. It’s a little too vague for my tastes (like “health of the mother” with regard to abortion), and the current pope has definitely come out and charged tribunals with the task of honing that definition to avoid the appearance of frivolous annulments.
Duress is also vague, but a “shotgun” wedding would certainly be eligible for annulment - whether it’s severe family pressure or coercion or seduction under false pretense.