It depends on state law, but the courts continue to hold marriage as an institution. Otherwise people would divorce under the laws of the date of marriage formation.
In addition child support could never be modified or altered without the consent of the married/divorced.
No fault is just that, ONE person decides the marriage is over and just swears that under oath, WITHOUT OTHER EVIDENCE, and the judge MUST (as a matter of law) grant the divorce.
How property and children are divided is a seperate issue.
Having children is irrelevent. No fault is a UNILATERAL petition. No consent required.
One of the claims was that no fault would prevent dirty laundry from being aired in the courts. Now it is even worse. (see the 1990's with rampant false abuse charges for legal advatage in custody matters.)
Evidently, then, such a marriage is a sham. But is it possible, if both parties want it, to get a civil marriage that actually IS a binding contract?