Sivir build path discussion / tips.

So I played some Sivir games in my silver account and in my plat account, and I pretty much keep playing her the same way; farm till I get the 3 core items and proceed from there. Till that point, I mostly try to hard waveclear and rotate around the map, pick as much farm as I can and keep towers safe while trying to push some towers myself. Also, I try to avoid fights that aren't 100% favorable, so that I minimize the risk of losing and setting myself back. Eventually, I keep the game stalled out while powerfarming and reach a state where I'm overly fed compared to enemies even if I don't have kills and it seems to be working fine.

Now, assuming this playstyle, I was generally going for Essence Reaver first, then Infinity Edge, then a Zeal item. I was choosing this build path because as I said, I'm looking to avoid fights and focus solely and pushing waves, which is why I get as much AD / crit as possible early on. But this last game, I came up with the idea: -What if, instead of finishing Essence Reaver first, I instead buy two B.F. Swords and proceed to finishing them as I gather farm?

The logic behind this is that Essence Reaver on its own is kinda bad, and needs other items to ramp up. For 3400, I only gain 70 AD, 20% Crit and 10% CDR, and honestly, all these stats, apart from the AD, are not really important early on. Instead, for 2600 gold, I can buy two BF Swords, which grant 80 AD, and adding a pickaxe to this equation, for 75 more gold compared to ER, I can have 105 AD. This means that waveclear becomes really easy at this point, since that's the AD that Sivir generally needs to start efficiently clearing waves with the 3 AA of the W and 1 Q.

For 3475 gold, I can stall out the game pretty easily, rotate through lanes to defend towers and farm up pretty fast. The mana regen / CDR / crit isn't needed early on since I can just back if I need mana, or I can just avoid fighting for the CDR / crit to be of any value.

Thoughts?