I'm pretty skeptical of your claim that the point of marriage historically was to force women to stay in the marriage. Evolutionary sociobiology holds the opposite: that marriage evolved to get men to stick around. A woman already has an evolutionary incentive to provide for her offspring: she's invested far more in them (having provided the egg and nurtured them inside her for 9 months) than her partner has. A man's evolutionary incentive is to spread his seed across more women, because he can have many children while his wife can only have one per year. But since society benefits from not having all the violence and uncertainty that results from men porking each others' wives and being unsure whether the children they were raising were actually their own children, marriage evolved.
If your "70% of no-fault divorces were started by women" statistic holds true, it could be because the greater economic power wielded by men made them pretty shitty husbands, and so when the opportunity arose, their wives divorced them.
Women are hipergamous, they stay only with one person at time, but they switch to what they perceive as better ones. Most divorces are early in the marriage, when the woman is still young enough to have her first kids, or more kids beyond her first or second kid, and thus they can still find another man. Also there is research that found out that divorce rates drop when a woman has male children ( but not female, and noone knows why )
If your "70% of no-fault divorces were started by women" statistic holds true, it could be because the greater economic power wielded by men made them pretty shitty husbands, and so when the opportunity arose, their wives divorced them.