Yeah, they should put pictures of electron orbitals next to the solar system one and say that we'll show how to derive them after the student has learned some Calculus.
It really p****s me off when journalists, and especially textbook writers, go on about how weird and mysterious some physics concepts are when the actual concepts have been non-controversial for decades in the physics literature. I admit it could be strange to a novice, but don't leave the impression that a little more background won't cure the metaphysical vertigo. Doesn't anyone know that Newtonian mechanics was just as weird for most people back then as Quantum mechanics is now? Heck, once someone REALLY knows how to do Classical mechanics, Quantum mechanics is a very small extension.
Like trying to explain a black hole to the average high school graduate – or journalist.
Although to be fair tunneling is a fairly non-classical phenomenon.
That is true (and easier said than done). The big leap (IMO)is accepting the probablistic nature of the wave function; once you do that, most of the problem is statistical-mechanical in nature.