I read that as the air density is lower at high altitudes, the scattering is less, hence the darker blue but then other colors are scattering lesser than blue, why don't we see a darker shade of the other colors?
Your physics is correct: All colors (wavelengths) that make up the "blue" sky are "darkened" with altitude in (approximately) the same proportion because there is lass air to scatter. However, the brain doesn't directly perceive how much red, green, and blue there is. The brain transforms this information into something like the "HCL" color space. "H" means "Hue"; different colors on the rainbow are different hues. "C" means "chroma", low chroma colors are washed out, zero chroma means shades of grey. "L" means luminosity, on a scale of dark vs light. If the red,green, and blue components are all reduced we notice less "L" but the same "H" and "C" (as long as it stays bright enough for cones to work).
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The sky is actually black. Check that for yourself at midnight.
So in the daytime, you are looking at a black sky that is "illuminated" by mostly blue scattered sunlight. The higher your altitude, the dimmer is the blue scattered illumination, so you start to see more of the basic black of the sky. You can test this on your computer display, by going to the color palette and setting it to full blue with no red or yellow. It looks blue. Now reduce the blue content number (often 255 max), and you will see the black start to appear along with the blue.
A very simple explanation for kids to understand is when there is less air (molecules) at higher altitudes, the air is more transparent, showing more of the black space. The blackness of space slightly darkens the blue to a deeper shade. At sea level, there is more air and hence less transparency to the black sky beyond our atmosphere.