Enslaving our children by forcing them to do household chores is highly likely to impair their happiness rather than promote it, and it does nothing to inspire them to work hard at things that matter to them.
Ultimately, we all (including our children!) have to do what we ourselves think best, what feels right to us ourselves, not what someone else says is right. We are all moral agents in our own right. When we self-coercively override our own wisdom and do what someone else thinks we should be doing, we are acting wrongly by our own lights. No good can come of that. Treat this site as a source of speculative guesses and interesting arguments, not as an authority you should obey.
It can take a little time for breastfeeding to stop being painful, but that is just the breaking-in period, like breaking in a new pair of hiking boots.