I think your title a word.
Going by the specifications the OP stated, games like WoW, LotR Online, LoL, TF2, etc. wouldn't be included. So my answer is as follows:
If a game is billed as a primarily multi-player game, then it doesn't necessarily need to stand on the single-player but if they're not going to put in the effort to make a decent and enjoyable single-player campaign, then they'd probably be better off making it fully multi-player to begin with.
If a game is billed as a single-player experience, or is the sequel to a game that didn't have multi-player and they're only adding in multi-player to 'appeal to a wider audience', then I think they shouldn't bother with the multi-player in the first place, because it's not going to tear anyone away from CoD, Gears, Halo, TF2, etc. for longer than a week.