A concept on items i haven't seen before.

I was considering an idea and id like to see what other league players think of being able to buy Finished items earlier, as in Infinity edge buy cloak of agility for 800 then finish it for 425 (it costs 425 with all component parts) but you don't get the 65ad from bf/pickaxe but you get 25% more crit chance. aswell as trinity force buying Sheen into Trinity for only 1383 but you only get mana and 200% power from items while the other stats are grayed out and get added when you buy them. I'm sure this could cause some rebalancing issues but I think it could be a cool concept into the game since someone with 6 items isnt that bad to deal with when 70% of there stats are missing while someone else has 3 full items. I was just wondering how everyone else felt about it since it seems pretty fun to me in mixing the game around and keeping it fresh.