Does it maybe have something to do with the fact that the people who would burn Barbies would be bothered about releasing the toxic fumes? And the gross pools of blackened pink gunk that would be left sticking to the sidewalk - kind of uncivic.

Maybe burning cardboard effigies of Barbies would work? Still not sure about the fumes from the pink paint. Assuming world stocks have sufficiently recovered to allow any to be sourced - didn't the Barbie set designers buy all the pink paint in the entire world, or something?

I guess the movie will at least be remembered in that way as the answer to a pub quiz question in future decades.