I think a lot of posters in this thread are confusing "something other than ADC/support in bot lane" with "no ADC". Way back when, ADC often went other lanes. Even today, depending on team comp and lane match ups, putting ADC in another lane is viable. As a counter-meta, the goal would be to have your "kill lane" or whatever bottom suppress enough CS from their ADC that their team falls behind.
Depending on the matchups elsewhere, an ADC can be a very annoying matchup in top or mid. Picture stuff like Sivir rotating mid against non-assassins, or Caitlyn top against some matchups. Then your mid --> bot Lux instead pairs with support Morgana and one bind = triple nuke all-in + tons of time in Morg's damaging pool, or other similarly dangerous combos. As long as your ADC has an equal-to-favorable matchup in another lane, you can easily do stuff like this without falling too far behind. ADC like Caitlyn and Trist are also tough to gank on top of it.
It's nice to have some AD near the dragon early in the game, but in practice in 99% of non-pro games ever dragon is something that 1) gets sneaked by a jungler soloing it 2) something taken early-mid game after a successful jungler gank bottom lane or 3) taken after a major team fight, and having ADC mid or even top would have only a marginal effect on objective control, if any. A jungler + mid laner + support that kills bottom lane could take dragon easily for example, same with jungler/top/support, and mid lane can help there anyway.