My kids have to do things that they don't necessarily want to do. Believe me, if it were entirely up to them they would never do their mathwork, or attend certain functions, and they definitely wouldn't do any housework or cooking. Nor would my son go to bed on time. :)
The difference is that their attending such things and doing such work is done willingly because we discussed and negotiated. They saw that either it was important to me, or that it brought them benefits over the longer term, or some other outcome. The idea that children cannot learn these things without having them forced upon them is simply false, IMNSHO.
For example, with housework, this fall when the learning year started I explained that I was feeling overwhelmed with so much to do and not having enough time to spend on Project Time (where I assist them with homeschool projects) and other things we wanted to do together. They love doing project time with me so they were willing to help out by taking on a couple of extra jobs around the house. They do not like doing housework, but they do it and I don't have to threaten to take things away if they don't because they don't feel that this was imposed upon them, but rather that they agreed to do it. If it's not happening we'll problem-solve: my kids both have sensory issues so sometimes it's a matter of choosing a different chore, or they may ask me to remind them to do it at a certain time of day because they are having trouble remembering, or they may ask me to help them break the chore down into smaller tasks so it doesn't seem overwhelming (I haven't had to do this, but these are examples of what we would look at if there were a problem). There are many reasons why something might not get done, but I never consider that they just won't do it unless I force them to by punishing or taking away privileges. The assumption is that we all want to find a solution that works, and so we don't give up until we do.
In other examples, they recently agreed to make their own dinners on Saturday night so I could have a night off. They don't get any obvious benefit from this - I explained why I wanted this, that a day off once a week would make me really happy, so we discussed it and they agreed to do it. They'd rather I made them dinner, but they see that it makes me very happy. And actually, they did end up having fun in the end, so they learnt another valuable lesson.
(I don't know why that is highlighted but I can't get rid of it!)
Even the most unschooled children encounter obstacles to their goals and desires. There is no way to live in the world without that happening. I do not have to impose such obstacles on my kids, they encounter them every day. Instead of being the artificial source of obstacles, I'm the coach that guides them through it. That is what I consider to be my role as a parent.