I'm saying it's the same reason why (x + y = z) should be illegal even if (x + (y = z)) is legal in any language. It's not specific to Python by any means. The target of an assignment needs to be obvious and not confusing. You don't want x + y to look like it's being assigned to.
There are two aspects I have been thinking about while looking at this: Introduction of non-obvious behavior (foot-guns) and readability. Readability is important, but I have been thinking primarily about the foot-gun bits, and you have been emphasizing the readability bits. I can't really accurately assess readability of something until I encounter it in the wild.
If the precedence was higher then you'd get a situation like
x := 1 if cond else 2
never resulting in x := 2 which is pretty unintuitive.
And you have to realize, even if the precedence works out, nobody is going to remember the full ordering for every language they use. People mostly remember a partial order that they're comfortable with, and the rest they either avoid or look up as needed. Like in C++, I couldn't tell you exactly how (a << b = x ? c : d) groups (though I could make an educated guess), and I don't have any interest in remembering it either.
Ultimately, this isn't about the actual precedence. Even if the precedence was magically "right", it's about readability. It's just not readable to assign to a compound expression, even if the language has perfect precedence.