Help Sivir Top

Early game, build Phage and start building into Zeal, usually just a dagger. Complete Black Cleaver, start building into Frozen Mallet. At this point, I buy Boots of Swiftness. Mid game, you should have BC + FM and Phantom Dancer. Late game, I build Frozen Heart(Deliberating between this or Frozen Gauntlet) and Blade of the Ruined King.

Plays very passively early game, using the spell shield to block CC or regain mana.

Now, obviously, this isn't a serious competitive build, but I'd still like criticism beyond "don't play Sivir top". While Frozen Heart supplies a huge amount of armor, is the area slow/bonus damage more valuable? Is it even worthwhile to be buying lifesteal, or would it be better to be building more damage(Infinity Edge?) or survivability? Although I would like those examples answered the most, any help would be great.