About EA making money I'd like to point out a few things :
Frostbite is extremely difficult to mod. That's well know for now.
Why ?
=> Because Frostbite has been designed first and foremost for MP games. Games that are in essence, not mod friendly for mostly balancing reasons.
=> Probably because EA (and DICE) does not want to be copied by other competitors. There are at least 3 big graphical/physical engines actually on the market : frostbite, cry and unreal (source is sort of an oddboy for me and does not belong to the same category) and it is very likely that EA does not want to give away their code, nor make it easily accessible.
On the topic of mods reducing DLCs.
I call this BS. Period.
Mods and DLCs do not compete. Mods could diminish DLC sales if mods costed money. Which is not the case. A game with a healthy modding community will have articles featuring popular mods appearing in the specialized press. For EA, this equals free advertisement and an extra purchasing argument. Why would they oppose this ?
All in all : losing the modding community will be detrimental for both players and EA, since EA will lose buyers, free ads and game lifetime. However to get mods back, we should rather pressure DICE and EA and convince them they allowing mods is better in the long run. In other words, what you lose in terms of competitive advantage over cry and unreal, you get it back with sales.