Certainly home life, economic background, etc have an impact on educational outcomes. But I'm making a narrower claim here. A student with a poor home life is likely to test poorly regardless, although the difference might be larger in some tests than others. But a student with the same educational aptitude may test better or worse depending on if they're being tested on topics that are familiar or unfamiliar to them.
Removing cultural context is certainly a solution. I'm not sure it's the best solution. Excessively-abstract problems are only one aspect of intelligence. Anything involving reading comprehension is going to have some linguistic or cultural elements, but I'm not sure it's valid to just remove reading comprehension altogether.
If you want to see a standardized test from a different culture, here's one that's made the rounds a few times. This is for eight-graders in Kentucky in 1912. The sections on Geography & Physiology certainly stand out, but even the math section has a notably different emphasis than modern education.
https://www.bullittcountyhistory.com/bchistory/schoolexam191...
I imagine other factors such as home life, economic status, and cultural emphasis on education would be much, much stronger predictors on IQ test performance.