There was a nice study of pre-K in Tennessee. People applied for pre-K , more than could be accommodated, so some were admitted (randomly) and some were not. Then the kids admitted were compared with the control group, those not admitted. This nicely controls for any systematic differences among volunteers, which often exist. By third grade the pre-K kids were doing worse, although I think not hugely worse. So pre-K is pointless (big surprise, considering that shared parental environment doesn’t affect smarts)- not that this or anything else is going to change James Heckman’s mind.
But then, I don’t think that most proponents of this kind of intervention have ever cared a whole lot about efficacy, because if they had, they would have run statistically powerful studies of the effects of pilot programs. I mean, it’s not as if statistical methods are a secret. If they were serious they would stop spending money on approaches that have been seen to fail and try to spend it on something that worked, or might work – but I don’t see that happening.