Why? Because the audience was in on the joke. It was a fun way for some of the characters to be fish out of water types while at the same time the audience is familiar or at least somewhat familiar (and in some cases, directly familiar) with the culture/music/character types shown.
How would an entire senior staff of a 24th century space station become so interested in this program?
- Step 1 - Bashir annoys everybody to death until they check it out.
- Step 2 - Odo voluntarily accesses the Vic program and spends a lot of time in the holosuite. Odo.
- Step 3 - After some time in the holosuite, Odo scores Kira. Odo!
- Step 4 - Everybody wants to check out this holosuite program!
- Step 5 - Like teacake, some of them are annoyed at first but eventually it grows on them.
Plus, those episodes were just a lot of fun and they were able to do some nice things with the characters. As for me, I loved Vic's character from the beginning, but it doesn't hurt that I actually enjoy that style of music from time to time anyway. I found him and the setting to be charming additions to the show. Now if they had a Kesha type as a recurring character, I'm sure I would have a different opinion.
My only problem with Vic is he highlighted one of the weaknesses of the newest main character - Ezri. They brought in Ezri and gave her the title of station counselor. I think they gave her one episode where she was playing the counselor role with Garak, but I don't remember much after that aside from a mention here or there. Vic actually became the station's counselor (he wasn't given that title, but that's what he became). He really became the station's counselor starting with "His Way," and then when he became a recurring character, that really became his function through the end of the series. And I loved it! It was certainly unique and worked well for a short run (season and a half). Much better than a Troi-like character for this setting. I think it worked well for wartime. But then Ezri was just there, sometimes pushing buttons on the Defiant and being more of a Jadzia type, and sometimes she was "just there." That bothered me a little. But there was so much going on by the end of season 7, I didn't let it ruin the show for me.