Why do people start Doran's Blade?

I'm having a tough time figuring out why people even bother to buy this item.

gives you +70 health, +7 attack damage, and +3% lifesteal, and leaves you with enough money to buy one .

gives you +10 attack damage, builds into other items, and leaves you with enough money to buy three .

Everyone I see who asks this question is met with the response that Doran's Blade gives you "better trades". I fail to see how this is true, if you consider that the extra pot and health from Doran's is equal to 220 health, while the longsword start gives you a total of 450 health in health pots, in addition to more damage. Unless both laners walk into lane and immediately get into an extended fight that results in one of them dying, the person who starts longsword should win out in the end with his superior damage and more effective health. Longsword also builds into other items, meaning no gold is wasted in purchasing it, unlike Doran's which must be sold later, which puts you ahead of the curve in itemization because your initial purchase was also an investment in a future item.

Caitlyn has a base AD of 50. Add the bonus AD from Dorans and runes, lets say we start the game with 65 attack damage. With 3% lifesteal, you're getting back 1.95 health per auto attack. This means you would have to auto attack approximately 115 times to get enough health back to equal the amount you recieve in health pots with a longsword start.

The other Dorans items give you some sort of bonus you can't get anywhere else. Doran's Ring gives you good mana sustain, and Doran's Shield shaves flat damage off of attacks. Doran's Blade is just a ball of stats you can get elsewhere.

So please, someone enlighten me. Why is Doran's Blade a first buy on ADCs and many AD top laners?