It is a left-over from Star Trek TOS. In it Chekov spoke Russian-accented English, so 2009 version wanted to reinforce that this is in fact same Star Trek, but better (IMO).
So in order to know how that happened one needs to go to ST: TOS and Jerry Sohl:
"We were originally going to have [each crew member] carry a language
translator, which would fit on the wrist like a beeper, and no matter
what area of the universe they were in, the thoughts that the people
were thinking would automatically be translated into English as they
spoke. We got rid of that idea, and assumed that everybody did speak
English." (The Star Trek Interview Book, pp. 127-128)
*After MemoryAlpha's entry under UT.
So by inference, the in-universe explanation was that ethnic (loosely understood here) background was cultivated and most people on Earth were multi-lingual still. Yes, UT was part of the comms protocols, also internal on-board comms, but apparently UT was more of a concept than an actual device. In other words: plot hole.