There's enough multiplayer experiences out there to make up for Bioshock skipping on it. I mean Fallout 3 didn't have a death match mode and the world didn't end. I'd rather they focus on a strong single player experience than water it down to half ass all powers to make a death match and 31 flavors of typical modes to an online shooter.
Games need to balance the characters for multiplayer or the campaign. In case of Bioshock, it's always felt like a series focused on a campaign, especially one where you steadily evolve into an unstoppable force of nature over the course of the game , it doesn't lend itself well to the multiplayer experience well. It's designed for you to be an overpowered being who wrecks waves of stuff alone.(while call of duty tends make you much more killable, and leaves all uber weapons for special scripted events or high level kill streak perks to even them out for multiplayer mode as you aren't remotely as power as the characters in bioshock.) You can't just translate those abilities wholesale (a game that did, Revenge of the Fallen didn't make forked modes seperate balance for campaign and multiplayer, and all flyers ruled the versus modes because they were just as mobile and deadly as when you tear up the AI. G1 starscream for the win!) You'd have to greatly water down the powers to balance it out or replace them entirely, at which point you might as well make an entirely new game balanced around the notion of a multiplayer style bioshock game from the ground up than try turn a sportscar into an offroad truck.
A game has to pick it's strength as it's rare a game excells at both competiative Multiplayer and campaign. I'd rather a developer picked their poison than crowbarred it in or just threw it in and said hey we did no balance it or put any effort toward it (like diablo2 ) and if you get horribly raped because you picked something underpowered for this mode not our fault. Plenty of games don't have competiative modes to them for multiplayer and I still love them. I love Megaman, Castlevania, Skyrim, fallout, bioshock , Mario, Final fantasy,Zelda, and many others that all lack any sort of death match or some other means of beating tar out of other players. It takes all kinds, and I love a good Co-Op game or death match not every game should try to be everything to every player. Pick your strength and don't worry about the rest. Sometimes less really is more, and this seems be definitely the case for game design.