For starters,it's banned in competitive play, so if you want to use that, it won't work.
Additionally, over Wi-fi, utilisation of such strategies may often cause other players to look down on you, since such strategies are strongly unadvisable and disliked.
Now what's the actual theoretical reason to not using it?
It's quite easy to block
Any Pokemon with Sturdy immediately negates the effects of OHKO moves. Fissure is avoided by any Levitating or Flying type. Guillotine and Horn Drill are blocked by any Ghost Pokemon. Shedinja trolls. Any Pokemon with Substitute puts OHKO strategies in a very very bad position.
How you ask? Substitute blocks the OHKO, and the Substitute fades. Considering the low accuracy of OHKO moves, it is more than likely that they will miss, giving free Substitutes and the opponent free turns to set up and attack.
The low accuracy factor applies even if the opponent does not carry Substitute. OHKO moves will miss 70% of the time - that means, 70% of the time you give your opponent a free turn. This can be utterly detrimental in a match against another Player - often they only need one turn of setup to sweep through most of your team.
In response to Terlor's answer, the effectiveness of his suggestion has dropped even further this generation. With the new mechanics of Infiltrator and Sound-based moves, it is so much easier to hit through Substitute, thereby reducing the merit of that kind of strategy.
However in fairness, do note;
You can still try using such a tactic if you are able to get your hands on say, Mind Reader + Sheer Cold Articuno or Mind Reader + Fissure Poliwrath. Or you can just yolo and try running OHKO moves straight away. It's really up to you, however personally I would rather make a normal team - it often works better, and people don't complain about it as much.