I completely disagree. It's not unusual to have three barb camps right around your capital. And each of them spawns one unit every turn for five turns or so. Until turn 30 I have seen more barbarian units than turns have passed. That's just insane. And you cannot switch barbs off completely because the AI will destroy you even faster than they do in any normal game.
Maybe I am just dumb, but I absolutely cannot understand how anyone could think this is "fun".
Well, I hesitate to be so argumentative as to speak with certainty for the experience of players on the whole, but I will say that the typical civ map suffers from having too many civ's packed too closely together. One consequence of that is that barb camps simply aren't afforded enough places to spawn to the rapacious degree you describe.
Now, yours is a fair assessment of a game I play when I find I have lots of land to myself, such as when I cut down on the number of civ's and CS's, or when I wind up being the civ at the bottom or top of a map with expanses of tundra and snow. And there are the jungly-heavy regions that have limited lines of sight. These are rife with barb camps. It's then when the overly generous allocations to barbarians can be onerous, because they will spawn a two-melee/one-ranged combo in one turn, and then upon any of those units dying, the barb camp will immediately replenish that unit, and thereby have an advantage in terms attrition.
As to how anyone can think such a situation is fun, it's precisely because it injects something brutal and chaotic into a game that is too often formulaic, plodding, and procedural. Players often feel like they're walking the bases to victory. AI civ's are often easy to placate, and even when they do go to war, they often fail to prioritize military units. So when barbs spawn, it's a welcome change in pace because you can't buy them off. All they want to do is attack.
Do try to always remind yourself that the barbarians tend to attack unto death, and when they don't have a ranged advantage (like spawning xbows when you only have archers. and must I again bring up the ancient-era quadremes?), then you can often fortify in defensive terrain and let them exhaust themselves against you. A warrior can outlast a barb horseman or sword in such instances with a +5 from a policy that you should certainly slot if you are suffering barbaric calamity. Don't press the attack any more than you have to. Camps do seem to slow down their spawn rate after seven or eight units.