I believe I have a good understanding of the phrase. But I need to be sure that I am correct.
"Takes no account of" can mean to disregard something or to not consider something. But I can't find a definition in a dictionary apart from Free dictionary that says, To not think about, consider, or pay attention to someone or something.
The Guardian has some examples:
The measure takes no account of leisure time, meaning that two countries might have equal GDP but one has workers toiling for 12 hour days and the other only eight.
GDP includes rough estimates for the value of drugs and prostitution, yet fails to take account of unpaid work in the home.
I need to say that something (e.g., the computation of GDP) knowingly and purposefully takes no account of something else (e.g., living standards, happiness, leisure time). "Disregard" is perhaps the right word.
It is quite different than saying John went out without his raincoat. He took no account of the fact that it would be pouring today. Here, John might have simply made a mistake and forgotten about the raincoat. He did not purposefully do that.