Education and Signaling

Is education more beneficial to the individual than to society? If most of the return to education comes from signaling, rather than from actual increases in productivity, then there is a case that the private benefit is higher than the social benefit. However, David Card says,

My reading of the evidence is that education is much more than a rat race, and that signaling effects--if they exist at all--account for only a small fraction of the private return to schooling.

Discussion Question. To justify public funding for education, should not the social benefit for education exceed the private benefit?