Why is 'Green Build' not a thing?

So there is the Blue, Red, even the Yellow Build out there. What about the Green Build?

These three would pretty much be core for any form of the 'Green Build'

Would make for a set for an offensive bruiser build.

Could even replace Death's Dance for a hybrid damage champion and it's still green.

This build would be rather difficult to afford as a support, but one of the more expensive offense items could be replaced by Face of the Mountain.

So, .. this item is admittedly not very green, but I really wanted to mention this as an item to consider because it is great for tank casters with mana issues. This item is pretty cheap and practically eliminates mana problems on it's own.

Of course for the Jungle role, Cinderhulk is green enough with any jungle item, but if you're really devoted, Tracker's knife is even more green.

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I absolutely understand that a build should not be exclusively picked based on item color, but given the previous items I mentioned, I actually think they work fairly well together, so much so that I am surprised that I can't find anything on YouTube titled "Green Build"