Not universally true. In many cultures, children are owed very little by their parents and are seen as a workforce and economic component of the family. The more kids, the more farm hands, the more secure the family is. Happy to direct you to some reading and sources.
Thinking parents "owe" their kids is a privileged perspective based on material wealth and access, compared to the rest of the world; also in terms of the culture and society you lucked into that allows you agency to live a free life.
I'm not sure if this is helpful, but I have a friend who has worked for rich people of various wealth brackets (multi-millionaires, multi-centmillionaires, and a billionaire). Their personal lifestyle don't seem to vary much, once you hit a certain wealth level, like multi-millionaire, you can pretty much get whatever you want,
But three things stand out: