Why do many graduate programs in mathematics (United States) still have foreign language requirements today (in 2010s)?
Just an anecdotal answer: My mathematics PhD program (at UC Berkeley) had a requirement to pass a language exam. This involved translating to English 1-2 pages excerpted from a mathematics paper written in French, German, or Russian (student's choice). We were given several hours to do this, and the use of a paper dictionary. 

I did not, and still do not, speak a word of any of these three languages (unfortunately). But I took the exam in French and passed easily thanks to the high number of cognates between mathematical French and English, context clues (being somewhat familiar with the subfield of math helps), and the fact that I had plenty of time to look up any words I didn't know in the dictionary. 

The main thing I gained from this experience was confidence that with a little extra effort, I could actually read math written in French. Since then, I have at times had reason to use this skill that I didn't know I had. 

I believe Berkeley math did away with its language exam requirement the year I graduated (2016), and I think this was an entirely sensible thing to do. But I would encourage all grad students to get some experience reading papers written in a language they don't speak!