This is the key point as to why this advice comes across to me as out of touch and patronising. Doing something where you have a real investment in the outcome

This is the key point as to why this advice comes across to me as out of touch and patronising. Doing something where you have a real investment in the outcome can indeed be rewarding and even energising, and even when it isn't going well that investment helps people to keep going; but for the vast majority of people work isn't something that they have any stake in, it's just a means to support the rest of their life and hopefully allow that to have a positive impact on their well-being. If you've no stake in your work, you're trying to balance the negative impacts of work with the positive impacts of the rest of your life, hence the phrase work-life balance. Having work-life harmony would almost certainly mean both work and everything else was equally neutral or negative.