However, I think it is fair that most people learn roughly what the side effects are of each line at a local level.
Ironically, this is an argument against many functional languages. There are not side effects of the logic, per se. However, there are massive implementation side effects that are not necessarily easy to reason on.
The saving grace for the vast majority of people is that typically you can get by without knowing all of this. The people that care, do care. But statistically you are not one of them. :)
That said I think the issues with assembly you mention aren't magic as such, they're just consequences of the commands. They don't really hide much (if anything) behind the scenes that you'd have access to anyhow.
It's just that CPUs do so much more than they used to.
You can think of assembly on those cpus as a high level language. It has little correlation with what's actually happening in hardware.
This is EXACTLY the same type of "magic" that is getting complained about above. The real implementation details are hidden and unknown, but the abstraction is useful.
I was just musing on how the arbitrary line is probably not as difficult to see as many other lines we have out there. I think this would fall into "systems languages" and related things.