It trades card advantage for tempo.
I can destroy any size minion for 1 and still slap down a dude.
This is the real answer. You can bust a taunt in an Aggro deck, and they are still scrambling to leverage answers.
This doesn't make it a great card though, for a couple of reasons:
1. It's poor in some matchups. Vs. Aggro, unless you're killing an aberrantly strong minion like Doomguard, it's probably not worth giving them more gas to fight you with.
2. Two cards is too many. Reasoning? Well, Sap gives them one card (basically) and it doesn't help them find a critical answer, it just stalls them a little. Letting them draw 2 may let them draw into an AoE (that critical answer), and increases their chances of finding that critical answer every turn afterwards, as their total decksize is diminshed. I wonder if it would be broken at draw 1, though.
3. Hearthstone is still often about card advantage. There is a reason Warlock is one of the strongest classes all around. Good card advantage is hard to come by in this game, so much so that people resort to playing Gnomish Inventor, and that a huge percentage of competitive decks play Azure Drake. Giving it away with Naturalize is not always a great move.
4. The tempo loss is not necessarily that great. When you naturalize a minion, you are essentially purchasing freedom from that minion for one or more turns. So, if your opponent plays a Shieldmasta, and you Naturalize it, and then they play a Yeti, you have essentially bought two turns of free swings from your minions on the table (as the Yeti then starts smashing your guys). This is a good scenario for the Naturalize player, in the reverse order (where a Yeti gets Naturalized and they followup with a Shieldmasta), the gains are non-existent. Unfortunately, this isn't what tends to make or break aggro games in my experience; it is if and how much AoE gets drawn. Naturalize actively works against you for the critical problems (see number 2.).
It deserves testing. It could be great if druid rush was more of a thing (it isn't, IMO, because we aren't talking about Flame Imps, Void Walkers, and the Warlock hero power). I just think the outlook is not so great, because the raw tempo it provides is ill suited to the kind of game Hearthstone is.
Take all this with a lot of salt. I've played a singleton Naturalize in a few of my decks, but haven't gotten to get it to really work. I haven't tested it extensively, as I'm not a hardcore druid player. It's also got potential in (or is the backbone of?) the mill deck, with Coldlight Oracle and Mukla, and all that jazz. I just don't imagine it's good in regular play, but by all means, experience and testing trump the best theory craft a forum visit can buy.