Speaking as a parent, there are plenty of options, some are really expesnive, and some cheap. You can choose which to pay for.
note that the things I listed above are fun, but won't get yoru children into a great college and thus won't ensure a better life for them and yoru grandkids. Choose wisely where to spend your money.
Avoiding debt was a good idea when interest rates were high. In the modern age where money is not constrained by scarcity, interest rates have been low. Banks have been loaning out the people's money at near 0% interest rates; often towards the goal of helping corporations to monopolize industries; if it was YOUR money, would you loan it out at near 0% interest rate? It doesn't even cover inflation, let alone the risk of default... Yet the government has been doing exactly that with the people's money; YOUR money. The situation has never been so generous towards borrowers and so bad for taxpayers.
Going to college used to be a good idea as it would allow you to stand out among your peers and guarantee you some sort of management/coordinating role. Nowadays, everyone has a bachelor degree and those who have a PhD are over-educated to the point that they've lost their sense of pragmatism. It doesn't allow anyone to stand out. Education feels like some scheme, disconnected from value-creation.
debt is note as bad as it used to be, but most people are not using it for things that grow in value. You talk about 0% interest - but a car loan has much worse payback rates.
College is free in Denmark (in fact you get paid to study).