Real chemistry starts with orbitals. Everything below is just excessive simplification that makes no sense when you go beyond very simple cases (taught in my country at the level of primary school).
You really could start with orbitals instead of shells and it would be as simple as the shells but made more sense and getting familiarized with them early would give you the right intuitions for tackling those more challenging cases.
Can you give me an example of a chemical reaction that is more intuitively understood with orbitals than with shells?
One aspect relevant to chemistry I can think of that can be better understood with orbitals is why shells have the size they do, but for that you need to understand Legendre polynomials, which I only learned in my second year of university, I think.
Orbitals tell you why the number of valence electrons is what it is, or why bound atoms form certain angles or why aromatic molecules make sense. Or they can even tell you why periodic table is like it is. [1]
To get introduced to them you don't need to know the math they are ruled by. Just seeing images of that model rather than shell model give you better intuitions about what's happening and more complex stuff isn't surprising and countrintuitive.
You really could start with orbitals instead of shells and it would be as simple as the shells but made more sense and getting familiarized with them early would give you the right intuitions for tackling those more challenging cases.