Parents can provide both knowledge and material support for various tasks related to home making and child rearing. It's nice to have someone who's done it before right there to answer any question and give you a hand rather than reinventing the wheel every generation. Splitting up chores more ways leaves everyone less exhausted, and allows for more specialization. You may not like your parents' style, but it's better than doing everything yourself.
The benefits go both ways. As your parents age, they become more feeble. Live in children can take care of their parents without spending a fortune on professional care services. Further many risks of old age like falls are greatly mitigated the more frequent there is human contact. Money that would have been spent on young laborers can instead be put towards retirement savings, again perhaps a macroeconomic loss but great for the individual.
Multi-generational housing is common in many societies. That it is uncommon in modern western culture is really an anomaly: the industrial revolution and subsequent scientific advances meant a sudden boom in the population and rapid changes in lifestyle, you couldn't simply have everyone stay on the farm their whole life, most people had to move to a city and start a new household. Now that populations are stabilizing, it makes sense that we would revert to the system we had before.