Investing directly, rather than through a specialised education fund or insurance bonds, gives parents flexibility to access a range of fund managers and equities that are available in the market.
If you want to invest directly into listed equities, then the option of regular contributions will generally not be available or will be expensive given the brokerage costs involved each time you buy or sell a listed equity. You, therefore, need to consider options such as allocating a certain amount each month to put aside to purchase the equities when you have a big enough pool to justify making the purchase.