Take Long Sword + 2 pots.
300 HP sustain + 10 AD
vs
80 HP + 5 HP per AA + 10 AD

=> you need 44 AA to get the same amount of sustain (but you don't get any control of your sustain with Dorans, so the first 10-15 AA could be worthless for sustain).
That means around 9 waves (5 CS per wave) and 4.5 minutes (6 minutes into the game).

If you lose one trade early with Dorans, you can't reg back easily, cause you need to AA. So a Dorans start can easily snowball the enemy into a decent advantage.
Pots are safer.
That was always the problem of Dorans. Less sustain and you need to be active for it.

And a small addition:
Dorans Shield > Dorans blade early.

If you get a perfect CS score (6 CS every 30 sec), you will gain 5 HP every 5 sec.
Dorans shield regs the same amount, but without the need to AA (so it is also good when you are in defensive mode).
Drorans blade gives also 5 HP per AA in trades, but Dorans shield reduced base dmg by 6. So instead of healing 5 HP, you lose 6 HP less.

10 AD vs 20 HP + 5 Armor (around 2 less dmg take nearly while 10 AD means around 7 extra dmg dealt)
Dorans blade wins there.
But if you consider that you still have the 1 less dmg taker per basic attack from above, the difference is 7 more dmg vs 3 less dmg.

that means you need to hit 5 basic attacks the come equal.

That makes Doran's blade better, doesn't it?
-> Yeah. But only if you make 6 CS every 30 sec. And that is a thing even the best players don't manage most of the time. You can heal back up through pushing the lane, but that is not what in most situations.

In the end you can take Doran's blade if you are sure you want to push or you are going to win trades and the lane early on (e.g. Cait).
If you have problems early, the new Dorans shield will give you more power to get to your CS (e.g. Vayne when you play against Cait).

I never ****ed with Doran's blade that much unless I was losing and needed the hp, but the +5 life gain actually makes it a good starting item now. I doubt I'll be stacking them since I try to be careful NOT to get hit, but if I end up pushing the lane, I just get time to back for me or my support.

As others have mentioned, this really doesn't help Irelia be the tanky assassin she's known for being. She has enough tenacity/escapability as in S2