Spherical harmonics are a good model for any spherical density function. You could describe the electron probability densities of a particular energy level of a

Spherical harmonics are a good model for any spherical density function. You could describe the electron probability densities of a particular energy level of any atom in terms of spherical harmonic coefficients. I think it just happens that hydrogen atoms electron clouds have particularly simple sets of coefficients so their density functions look a lot like the raw harmonic bases. That’s more because hydrogen atoms are simple than because of anything profound. Like, when something vibrates in 1D, if it’s simple (like a mass on a spring) it will move in a simple sine wave - the Fourier coefficients describing its behavior will be simple, because it is simple. But if it’s more complicated (like, a lump of jelly on a linked set of springs) it will move in a complex wave, with complex Fourier coefficients. Its behavior will be complex because it is complex. That hydrogen electron clouds look like these lobed shapes then is as unsurprising - or possibly as surprising, depending how you feel about the unreasonable power of mathematics I guess - as the fact that a weight on a spring follows a sine wave.