Actually, I believe requests can be taken and played during certain rare occasions...
I remember when KZON first converted from talk to rhythmic and I wanted to test to see how far they'd go with their "rhythmic" label, I requested "love you down" by Inoj. This song was not on the playlist at all, ESPECIALLY for an urban sounding station (which it was very much so at the time) in Phoenix. The lady who answered said she'd see if she could get it in there next. To my surprise, she got it in there as the next song!
It has never been played again (outside of a pre-done back in the day noon mixshow from a dj who did specialized mixes for certain stations) on that station, and despite the fact they are showing more of their rhythmic side now, it would most likely not be played if it were requested again today. It was funny because as the station was still new, they had a very limited playlist of only modern rhythmic hits, then out of no where, "love you down" by Inoj from 1997 pops up.
The last times I ever got a request played that was not a normal radio song was when I requested "Until tomorrow" by Adriana during the Power Workout at Noon mixshow in 2000 and "in a dream" by Jossette on 103.9 KPTY which was supposed to be a mixshow only song. I used to request Jossette every single day after getting home from school, around 3:10 - 3:30pm or so. After a while, they ended up ONLY playing "in a dream" between 3 and 4pm for about a week and a half. It was funny because even though KPTY was rhythmic, the song and the version they played was very awkward for the station, especially when it was all hip hop and r&b, then next thing you know, Jossette pops in. By the way, "In a dream" starts off with a house beat, runs into a main breakbeat with acid electro sounds (similar to "set you free" by Planet Soul), then ends with a house beat. I don't know of any other stations that played Jossette instead of Rockell "in a dream" as a regular rotation artist.