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That's a really interesting question. I think it is because that Hydrogen is a really simple atom with one proton and one electron (which makes examples easier), but I'm curious to hear what other people have to say.
To make this simpler, one can just look at the ionization energy of the H atom. The H atom has one electron, and so calculating the ionization energy (using coulomb's law) is much much simpler than calculating the ionization energies of atoms with multielectron systems. Although we are not performing rigorous calculations relating to ionization energies, the concept still holds that the simplicity of the hydrogen atom is much better for understanding the fundamental concepts of periodic trends, photelectric effect, etc.
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