They actually pulled most of their top titles off Steam when Origin launched. Mass effect, Dragon Age etc. If you already own them on Steam then they remain in your library but you can't buy them on there anymore.
For Dragon Age 2 and Mass Effect 3, I agree with their reasoning. Steam doesn't allow in-app purchases that circumvent their distribution system, and that's a load of crap.
The idea there is probably something along the lines of preventing developers from selling their game for $0.99 and "unlocking" it in-app for $59.00.
The no in-app purchases which don't cut in Steam was introduced when they began allowing free-to-play games on the service (which are usually monetised by microtransactions, and would be a money-loser for Valve if they didn't make a cut from them). I don't know why Steam can't make an exception for EA titles (or those purchased from the store rather than F2P), but that's the reasoning.