But for everything short of perfect, this measure is useful as it shows whether false positives or false negatives dominate.
What would it be useful for and do you need that specific ratio for anything?
Because unlike many of the other rates, ratios and indexes, this one isn't really very suitable for tracking, comparing and optimizing towards the goal of increasing TP or reducing FP or FN.
Instead this only looks at the ratio of FP and FN. And to be honest it also looks like a rather complicated way of doing it. So if you're just interested in what number is bigger... Well look at the two numbers and it's right there. Or why not just take the ratio FN/FP or FP/FN which already tells you the factor of difference.
But most importantly that ratio is usually not of any significant interest of it's own. Like primarily your focus would be to increase accuracy and to reduce the overall misclassification and after you've optimized that to a comfortable extend you'd usually have a preference for one kind of error.
So idk suppose you make a test for a disease then false positives are better than false negatives, as you'd rather expend more care on people who don't need it than to have ill people run around and further spread the disease. While for example if you're producing billions of screws per day you're preference might be towards minimizing false positives because it might be less costly to discard perfectly good screws than to pay for the damages caused by faulty screws.
It's rather rare that your priority would be to regulate a specific ratio between two kinds of misclassification. Especially when this really just regulates the ratio of errors and not the overall prevalence of errors. So let's say you want a ration of 60% FP and 40% FN, but you have 40% FP and 60% FN. Then one way to optimize would be to increase the overall amount of errors by adding false positives until the ratio fits.
That would be completely counterintuitive with regards to any real world example. So rather than trying to optimize that you'd rather look at the max(FN, FP) and then try to improve the respective sensitivity or specificity score while checking the other for growth.
So even if you were interested in that ratio you wouldn't really be able to use it to track that progress, would you?