I wanted to throw my hat in the ring about this issue.
I initially mis-linked another Steam account to my EA account, and never noticed. That was until I purchased It Takes Two to play with my girlfriend. I went to launch from Steam and Origin told me I had a different Steam account linked so I couldn't open the game.
So I went to my EA account page, un-linked the Steam account and attempted to link my current Steam to my EA account only to be met with the error message stating I can only have one Steam account linked to my EA Account in my EA accounts lifetime.
While looking online for a solution I found this thread and spent the next 2 hours reading it in it's entirety. It's abysmal that EA forces you to launch Origin even though a game was bought on a different Platform. If I wanted to play the game on Origin I would have purchased it through Origin. On top of that, the also abysmal policy of only linking one account per type (Steam, Xbox, PSN) to an EA account.
Even if one of the other repliers is right about key exploiting being the issue for this change in policy, EA should have given their support team the tools to fix it from their end.
I hope this issue gets resolved soon so I don't have to refund this game since me and my girlfriend are both excited about it. But I don't have high hopes considering the silence from EA Staff members here but also EA's track record.
I would have opened my own thread before finding this one, which I'm glad I did because I agree with everyones sentiment here that the more concentrated noise the better. Even if the platforms trying to be linked are different, it's better to be all in one place.