First off, I want to say that I totally agree and disagree with you all at the same time. I have played Yi for a very long time, and I have tried AP, AD, and hybrid. They all work very well, but you cannot compare them apples to apples, because they both strive to do different things.
This is the end-game pushing Yi. Whether you like it or not, AD Yi has the best chance of pushing towers, especially when you can crit over 811 Attack Damage with over a 2.0 AS. Combine that with your E and your R, the turret will be a goner. Not to mention how effective this is against other players. Add in life steal, and you suddenly become a major threat to the people who try to engage you. I once took on 3 lvl 18's (I was 18 as well) and had about 300 HP to start, and ended with close to 1000 HP. They all died.
This is an early game farming Yi. Not going to lie, but Yi's Q and W have such a kick-ass AP ratio that as long as you have mana, you never have to leave the lane. Not to mention the .5 seconds that you cannot be hit upon activating Q, you can really piss people off. However, when it comes to mid/late game, the problem I see is that you run into a massive problem, COOL DOWNS. Because your Q move is the only move Yi has to deal AP damage, and because it is on a CD, there is no way you can spam it. So you either become the assist champion, or the KS champion (the latter really pisses people off, trust me). Most of the time, you will use Q, and then end up losing the kill to someone else, which really sucks.
Good for team fights mid game, but cannot effectively push turrets or stay in lane, and costs a tremendous amount of money to afford. Really a waste of time.
MY OVERALL VIEW:
If you want to truly rip people to shreds, build AD Yi, focusing on getting 100% crit, some life steal, and a ****- ton of AD. This build only fails when games end quickly, but if you farm and hang in there, you become OP by the time you get to the 30-40 minute mark. My build sounds really crazy, but this has worked for me:
3) Infinity Edge
4) Phantom Dancer
5) Phantom Dancer
6) Infinity Edge
*Please note, I do not build these items in this order, but this is the final product.*