He was 19 or so in 2004 when it was current in pop culture, and it became his “thing” to the media. That crazy Ryan Lochte, with his blinged-out grillz yo. Isn’t he whacky. The media have an extremely limited attention span; they’re basically able to remember one trait of a person. That’s his.
So now he gets more media attention if he plays up the grill. So… he plays up the grill.
And, to some extent, he and Phelps and the others are kind of living in a bubble. Pop culture may have moved on and Nelly is no longer relevant to the masses, but people with crazy Olympic training schedules don’t really get out much to catch up with the hoi polloi. So Lochte doesn’t know he should be shamed for still liking Nelly, and Phelps probably still likes whichever rapper he used to be into.