While investing only for the match may be viewed as shortsighted, it does help solve the long-term problem by funding their retirement. I envision a plan were the match is regressive based on the parents annual income. Those parents in lower income brackets would have a larger match than those in higher income brackets. In all cases the match would be limited to some dollar amount per child per year. This program would be open to all brokerage firms, mutual funds, banks, insurance companies, etc.
Private firms are most capable of getting the word out quickly.
They would also be required to report net contributions to the State on an annual basis. The State would match the contribution based on the regressive income scale. The States contribution would be held in a separate account and eventually paid directly to an academic institution.