Sheldon Brown, the departed patron saint of FG conversions, made the case that old bikes that otherwise would have been scrapped could become useful bikes again. In that spirit, the bikes I've converted have been mid to low end yard sale and sparkle day recoveries. If the bike needs major repair and overhauling, and when you're done it will still be a mediocre bike, why not convert it?
On the other hand, if it's a viable, good bike that just needs freshening up, it would be a shame to butcher it. I can't imagine what kind of knucklehead would take a bike like a Colnago or Paramount and turn it into a clown bike.
I used to enjoy the Fixed Gear Gallery, but the bikes have all become embarassing self-parodies. One hipster toy after another "rockin'" deep V wheels, ugly paint, goofy riser bars & grips, and a Brooks saddle. PBR's, piercings & tats, plaid shirt, skinny jeans, horn rimmed glasses, short brimmed hats, messenger bags. What a cliche'!