Sorry OP, RNG doesn't like me already as it is.
Original thought, terrible idea. What you are suggesting means that a person with luck doing normal modes is gonna have better gear than a person with bad luck clearing heroic mode, be it due to itemisation or stat-budget, itemlevel aside. Not even to mention the fact that the mere thought of the odds you'll get that perfect, if only good, item will be enough for most min-maxing players to just give up on the spot.
It's hard enough to even get the items you need to drop. With this idea implemented, you cheer because it's the item you wanted, and then you're disappointed because the stat generator let you down big time.
Loot is so limited in WoW, it's not like Diablo where every mob drowns you in yellows and every pack seems to drop a legendary at high enough paragon levels.
I don't think it's that bad of an idea if the range of values was much smaller. 700-1200 is far too big.
No more than like a 1-2% difference I think would be sort of cool in the idea that you could get a "perfect" one, but getting one on the low end wouldn't really be much different. Of course then you start getting into the "why bother" territory when the impact is so small. Don't think the development time would warrant it.
Something I think might work out better maybe - if you could, after getting an item, spend something (a small amount of valor perhaps, gold would make it too easy to keep doing it) to take a "gamble" on the stats of your item (that you already have), or just one stat. Sort of like reforging, but could be good or bad. It would "randomize" that stat within a + or - 30% range of the original value of the stat.
players get enough screwed by rng no need to make it rng^2....
Already happens on some blues and greens, on pre-71 gear at least.