Why are mages sometimes played bot instead of traditional ADCs?

ADCs tend to have a very clear path to success: Survive the early game, start getting strong mid-game and be an absolute beast late game.

What happened is that the "stereotype" was made even more evident. ADC's early game items were nerfed while late-game items were buffed. Furthermore Support items were buffed, towers were made weaker and overall games ended faster.

This in turn meant that there was no reason to keep a traditional ADC as chances were, no ADC will get the chance to get enough items to pull its own weight. Next logical best choice for heavy damage from range? Mages with constant high DPS, such as Ziggs.