I'm sure that that blob of code would much more legible if it was better formatted.
Whenever I help novices with their code I ask them to transform all their cells that are not oneliners into code cells which require manual indentation.
But the frightening flexibility of the Mathematica language certainly doesn't help.
As to the question if you have to be a developer to write that kind of code, of course not, but you do have to be an experienced developer on that platform. I for one really like Mathematica despite the closed source and the offputting look of the source code, exactly because you can do the sort of magic shown here and actually get there pretty quickly.
Now, I hope that didn't sound too defensive :)
"To be fair, mixing meth and display logic in a giant function like that is a bad idea in any programming language."
Frankly, I agree with either statement.
I've been using a TI nSpire calculator on and off for math and it's pretty decent with respect to readability on the input and output side of things:
https://www.youtube.com/watch?v=PpmpFis8RQM
Even carries the input/output semantics into the programming language:
https://www.youtube.com/watch?v=oTdvIm9coXk
(just skip around the videos to see the input/outputs)
x^2+2x+1 = (x+1)^2;
If x=-1, then (x+1)^2 + 5 = 5
TreeForm[ x^2 + 2 x + 1 == (x + 1)^2]
+1. And it gets even more easier to read (“read”? :-) when you can select pieces in FrontEnd, with multiple mouse clicks or a corresponding hotkey. I got so used to it that I actually developed phantom pains in my editing of Html or TeX (or whatever, for that matter).