Whenever I hear a news article that there is no X gene, I am completely unsurprised. The idea that a single gene would uniquely determine a particular trait, as if it were a variable in a program like "bool has_blue_eyes", seems oversimplified and unrealistic.
Sure.
Sickle-cell anaemia is one classic case, one (recessive) gene.
Huntington's disease is another, it's about a specific repeat number.
But, as you say, most complex traits (such as height) aren't like that, and involve hundreds or thousands of different genes. IIRC eye color is actually fairly simple, not one gene but much of the control in just a handful? Maybe hair color too? (But not super-sure.)