I think children should do enough chores to have a sense of self-efficacy. Same with survival skills. Being college-age or older and not knowing how to cook or do basic cleaning is an embarrassment, even if you're rich.

All that said, if you want your kids to succeed in the world, they have to know how to do a task without becoming the one who does the task, if you catch the distinction. In the workplace, you have to be willing to do unpleasant jobs, but be extremely selective in what you're willing to let yourself become the one who does. Outside of the upper class, no one really learns this skill. People from working- or middle-class backgrounds are either too resistant to doing tasks they consider beneath them (which is a bad look) or too willing, which leads to recurring time and image costs that eat up their ability to have a career.