you pick leblanc because her damage is almost 100% unavoidable. between her point click q, her r, and her quick moving high damage massive aoe w her damage is almost impossible to protect yourself against outside of buildpath and counterpicks. also, her mobility is incredible, she isn't very mana hungry, she has good damage at all points but lvl 1, she has her e for some nice cc, low cooldowns. sure she's squishy, but you have to actually catch her first. people pick her over ahri, fizz, zed, and akali, because her damage is much more instant and she can get in and out at the same time; kinda like zed and veigar had a baby. as for what you said about backing after losing trades, you have to lose trades for that to happen, which leblanc very seldom does against all but tanks and silencing champs (or high high high sustain champs). about what you said about lack of mana, energy is actually a more limited supply than you think because most energy champs spend their full bar with their full combo, and it takes a while to get it back up, so you cant do much after its down. also, leblanc doesn't have much of a mana problem aside from the very start of the game.
going back, about what you said about it being impossible to trade with leblanc vs ahri, note that you said what IF ahri lands her charm? she has to land it, and its really not too difficult to dodge. leblanc can q w you and you cant do crap about it unless shes retarded and manages to get juked out of her massive aoe w. personally, I don't play her literally entirely because I think shes a douchey champ and I don't like playing douchey champs. however, I have been told that she takes a surprising amount of skill, but I would guess that shes one of those champs that just takes a little while to get used to. just my 299999 cents ;)