AP Yi bot is a pretty powerful option sometimes, and really shines if the bot laner doesn't have strong or reliable interrupts for Meditate.
The trap that many people fall into, though is building poorly and failing to maximize his damage. Tripen (Haunting guise, Sorc Boots, Abyssal) DFG, FH, Deathcap has been a build that has been working for me, as it maximizes CDR and Mpen, which is important for actually clearing the minions. I feel that too many people get too aggressive too early with AP Yi, which doesn't work on his bot lane until very late in the game (after deathcap).
If I had to hazard a guess as to why he seems to get picked a lot, it's probably because he costs 450IP, and nearly every summoner owns him.