Both core counts of the argument are wrong, imo. The threat of barbarians - raiding and pillaging and the like is realistic and historical enough to warrant inclusion. Other "civilizations" simply cannot represent this type of interaction between peoples, because they cannot raise and maintain militaries quickly enough or at great distances. Since we can't really allow opponent civilizations to suddenly gather up a horde of cavalry and ignore the normal maintenance/economic costs - though to realism maybe that better represents, say, the Mongols - a neutral/third-party faction is reasonable.
Now, it may be argued that the way barbarians are implemented in gameplay is not historical - and yes, I can agree with that. Civ5 does appear to have incorporated and improved upon ideas from previous games though - reintroducing barbarian camps, which imo were the best system rather than civ4's random spawns, representing temporary yet significant threats to a civilization. And then the introduction of minor city-states, which aren't viewed as "barbarian," is another plus for realism.
In terms of raw gameplay though, barbarians as they've existed throughout the civ series serve absolutely vital purposes. Games without barbarians play immensely differently and the game is very much balanced for them. Civ4 animals for instance, certainly stretched realism and historical accuracy but only because the gameplay intention was also crucial - to place checks on expansion and require investment in military forces. Not that the best players couldn't get around it, but it was there for a very good reason. (in civ4 terms I would have favored having most barbarians represented in a better event-based system for later spawns after perhaps initial warriors/animals. But new combat mechanics and camps and all change that anyway in civ5)
And if you want better examples of barbarians' usefulness in immersion and gameplay, some mods do excellently - you'll never dismiss them entirely if you've checked out some great mods on the site here, like FFH as one of my favorites.