Okay here's my take: the Barbara Dex Award deserves to go to the outfit which most hindered/mismatched the performance/song and made it the hardest to transmit what was good about an entry. Using those criteria, Conan and the stiff, heavy fabric he was wearing deserved to at least contend for Barbara Dex because the outfit made it harder for him to communicate the buoyancy and energy of the performance.
HOWEVER.
I know full well that the hindrance the outfit provided Conan had roughly zero role in winning him the Barbara Dex Award. I'm dumb but not that dumb. He would've won Barbara Dex wearing just about anything he would realistically wear onstage. Heavy Barbara Dex Award voters OGAE are simply too basic for that not to have been the case. Besides asking for an OGAE number while voting and discreetly throwing votes that come attached with one into the trash, which wouldn't be fair either, I don't really know how the Barbara Dex Award can stop being anything but a badge of honor in practice. Until better minds find a solution, I salute Conan and his award-winning fashion choices, problematic as I found the one he ultimately made.