Activate a Product on Steam...?

I know about adding Non-Steam games into library and have seen all the forum posts asking how to "transfer/receive" Origin game's too Steam. I've looked everywhere for the location of the digital product code's (CD-Key) for the title's I already bought and cannot find them. I should be able to use my Battlefield/Battlefront CD-Key's to activate product's on Steam. Since Origin is a required must to play the title I bought through Steam anyways, there should be a way to activate the products on Steam. 

Everyone that says "It makes no difference" does not use Steam as their main source for gaming, yes, there is a difference. People like collecting the Steam Cards and use Steam's built in features, they even advertised the use of the "Workshop" for some titles.

So why can I not find the product codes for any games in my library and yes I looked into "How to find the product code" on EA's Help, but the code is not visible for any of the methods used to find said code.

For physical copies or bought on other launchers (GOG,U Play, R*) I was able to activate the products on Steam using the Product Codes provided after purchase to add to my Library, so why not with Origin?