There have been multiple studies done that prove that studying the arts/humanities make better thinkers of the scientists. I don’t know if they will be helpful, but here is a couple of links to articles on this:
https://theconversation.com/steam-not-stem-why-scientists-need-arts-training-89788
https://www.primotoys.com/blog/2017/06/steam-to-stem-the-importance-of-art/
There was one thing in your post that caught my attention. A CM education is not child-led. In Charlotte Mason philosophy, you are feeding a child’s whole mind. Just as you nourish his body with a healthy diet of varied veggies, fruits, proteins, grains, legumes, nuts, etc., you nourish his mind with beautiful images, wondrous math concepts, lovely music, adventurous literature, up close and personal nature study, the grand pageantry of history, various branches of science, fun and stirring poetry, learning to draw, life skills, handicrafts with a real purpose, and more. Nourish his soul by teaching him about God and helping him to have his own relationship with him. Nourish his emotions by being with him, loving him, and introducing him to all the wonders of the world in a safe environment with a guide that wants the best for him, which is you! But you are introducing these things – he is not picking and choosing. In many ways, he must be taught this wide variety before he can make an informed choice.
Each of these fine arts help your child to develop a lot of unsung, but necessary, skills for life: attention to detail, discipline, empathy, emotion, discrimination of taste (truth, goodness, and beauty), critical thinking, and more.
Nature study actually lays a very strong foundation for the sciences as they get older. Spending time observing nature up close and personal lets them develop relationships with various animals, weather and plant patterns and more. Then as the technical names and terms are introduced in higher sciences, your child will have real life understanding of the topic. CM called it giving names to old friends. As your child grows and matures, you introduce him to wide varieties of sciences: CM taught Botany, Geology, Astronomy, Chemistry, Physics, and Biology. There are others, as well. Nature study will have prepared him for this.
As your children get older you add in other subjects like literary analysis, logic, economics, government, etc. You add in the higher maths and sciences.
And really, CM does not advocate that you have to understand everything the way our educational models do. It is enough to introduce children to something like a beautiful painting, a lovely piece of music, or a poem or story and let them take what they will from it. And I promise that they do. You will learn, too. It is kind of like being a new parent with a brand new baby and growing into the whole parenting thing with the child. 😉
The whole gist of this is that as you spread the wide lovely feast of subjects – both fine arts and more logical ones – before your child, he will have had exposure to lots of ideas and he will find the ones that truly speak to him and nourish his soul through out his life, not just in a money-making career.