I like the idea, I'm not against it.
You can still find any items you might want to pay for by yourself simply by playing and being lucky. That's what Diablo 2 was about, and that's what Diablo 3 still is about, it's a form of gambling, risks and luck. If you want a "shortcut", see some item at the AH that you think you might "never find" (which is virtually impossible, there's always a chance to find it, you never know), it's super rare, then you can buy it with in-game Gold or real money.
The thing is that item you bought is part of the game from the start. It's not a form of micro-transaction that would otherwise grant clear character stats, power or other means of advantages exactly because what you'd pay for wouldn't be in the game "normally". For example, I played Allods Online (I haven't touched it in months), you can technically play the game for free, but the micro-transaction system is pure scam and clearly gives advantages to people paying real cash to buy the "cash shop" currency (gpotato). You can get an extra earring slot to equip a second earring (giving extra stat points), you can buy extra talent/skill points, you can buy powerful trinkets, superior rank mounts, offensive mounts (can fire at targets or charge at them). You can upgrade your runes at much higher levels than anyone grinding to do that for free (giving direct offensive % advantages and defensive advantages in the form of damage reduction), etc. You CAN "grind" for MONTHS to manage to buy even half of those advantages if you really have no life, because you can exchange in-game Gold into cash shop currency without paying real cash, but that's more of an illusion rather than being actually practical for everyone. To rely on that currency exchange system and becoming "good enough" for end-game PvE and PvP you would need daily (and hours each day) game-play dedication for months (if not more than a year). It's not "just" for shortcuts concerning leveling your toon faster than others, or buying vanity items (those things are fine), it's that, but they also include "incentives", you pay real cash? You have a better (or much, much better) character than others' in return.
Now, in Diablo 3... say you want to buy the Immortal King set's Hammer (let's pretend it's super rare on paper, the actual chance for it to drop, on paper, is very low), you COULD find it by yourself in the game, it's already there. That IK Hammer is NOT an "advantage" because you bought it with real cash, and does not only exist on your character because... say... you'd have bought some DLCs or something giving "exclusive" items. To buy that hammer with real cash is only a time saver, time is money, literally so in a game like Diablo 3 (same thing with D2's third party items sellers everywhere on the web). That's why I absolutely don't give a damn about that Real Money Auction House, it's just a way to cut corners, save time and take shortcuts to get specific items that you wouldn't want to bother trying to find yourself by simply playing the game.