Child abuse is 40 times more likely
when single parents find new partners.
Children living in homes with unrelated adults are nearly 50 times as likely
to die of inflicted injuries as children living with two biological parents.
Obviously, doing something that raises your child's risk of maltreatment or death is abusive. But it is not reasonable to order adults to refrain from leaving bad relationships or to abstain from sex/romance after leaving. I also don't think it's going to be very effective just expecting people to ignore a very potent if subliminal evolutionary drive -- it's quite common for animals to injure or kill unrelated offspring. If that would work, we wouldn't be seeing these astronomical increases.
I think the best solution is to build better relationships in the first place. That is, return to serious courtship. If you want to screw around, that's fine, but don't make babies while doing it. First find a partner, then get married and make a home, then have kids. Today, people often do it backwards. That's not a great way to make a life, and apparently it's a great deal more dangerous to the kids than expected, beyond the usual heartbreak, upheaval, financial wreckage, and lost fault tolerance. If people put in the effort to make solid relationships first, that would greatly reduce the number of kids living with unrelated adults, and thus lower the risks.