According to Kaplan (GMAT tutor) the following sentence is correct in GMAT land .
Proponents of the equal rights amendments argue for its necessity if only because averge salaries for women are still considerably lower than those for men with comparable jobs and work experience.
"if only because" is correct, yes.
Proponents of the equal rights amendments argue for its necessity and perhaps they do so for the sole reason that average salaries for women are still considerably lower than those for men with comparable jobs and work experience.
"if only because" is purely idiomatic.
I clean the kitchen floor because it's dirty. = I do the cleaning for this reason: The floor is dirty at that time.
I clean the kitchen floor only because it's dirty. = I do the cleaning for this reason, and only this reason; I don't do it for any other reason: The floor is dirty at that time.
I clean the kitchen floor once a month if only because I've gotten into the habit. = I do the cleaning for no really good reason. I do not do the cleaning because the floor is necessarilydirty, for example. Maybe IF I do the cleaning, the real reason is ONLY/simply/just BECAUSE I'm in the habit of doing so, whether the floor is dirty or not.
However, there is just one more slight nuance of meaning in "if only because" which I feel your "translation" does not capture.
I clean the kitchen floor once a month for no better reason than that I've gotten into the habit.
The sentence just above seems to capture the meaning just a slight bit better, to my ear.
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Another related idiomatic pattern with "if" is as follows:
If I clean the floor, it's because I'm obsessive.
We could almost call this "non-conditional if", because it really is just a fancier way of saying "I clean the floor because I'm obsessive." It certainly doesn't mean "If I clean the floor, I'm obsessive" nor "If I'm obsessive, I clean the floor."
Now you understand the usage if only because you have discussed it and thought about it for a while!