Even having a separate PVP mode would create this insufferable situation where the people who "opt out" of PVP get trashed by the people who do play PVP, and the massive epeen peacocks strutting around would be even worse than they were during the hey days of this forum.
Don't get me wrong, I like PVP. I don't even mind PVP communities that much. But I also like having a game I can play and by extension a gaming community that, while not entirely free from epeen/eboob and competition, is largely and solely built on top of a co-op experience. I like to go to other games for PvP, I like to come to Mass Effect for co-op.
This. Also, as some people said previously, it does not make any sense with regard to lore, at least for ME3. There are reapers/geth/cerberus/collectors who want to reform/kill/subjugate/convert all advanced life forms in galaxy and these are the enemies. PvP just does not fit in unless we have an option to play as reapers/geth/cerberus/collectors and we don't.
I have no idea what MEA is going to be. It might be less polarized (good guys vs bad guys) and PvP might be more appropriate lore-wise.
IMO, PvP community does not have to be unpleasant by itself just because it is PvP. Different types of games attract different people. I have very positive experience involving Civilization mutiplayer by being myself an active participant and by policing these types of communities. Civilization is a turn-based strategy game but MP has a rather tight timer which makes all versions of Civ more RTS-like. Civ communities however are substantially different from other RTS communities as the game is quite complex and deep and requires extensive knowledge and clear rules for anti-cheat control on semi-pro and pro levels.
So, if PvP in MEA has strong policies and good asset management, it would work and would attract a lot of extra players to MP. There are a few mandatory things though IMHO which should be heavily enforced. These include absolute balance of various characters and weapons (cannot have characters aka stunlocking Novaguard level 100 with acolyte X versus no dodge fat Turian level 10 with avenger I), strong cheat protection, fast and efficient ladder admins who are not hesitating to permaban people for bad behavior or exploits, cannot have additional powerful gear/unlocks which are bought with real money (ideally everyone should have some basic gear/weapons specifically for PvP mode that cannot be modified), and there should be no effect of ladder position on the game as experience with PvP by itself is enough of a handicap for newer players. It means that anybody who just started has a fair chance to beat ladder Number One as they would start the match with the same stats, weapons, and gear. Also-also, it requires dedicated servers which can check pings and packets to ensure all PvP have similar speed and reliability of connection. Otherwise, hosting would be too much of an advantage or disadvantage. Also-also-also, no grinding, no manifest advantage, no horrible DAIMP god-mode promotions and other similar crap.
I know, all this sound too idealistic and might not be practically feasible.
tldr: PvP might be interesting under the right circumstances.