I played like this long time ago, but i kinda think now, that is a noob trap.
BONUS 1
You get culture from barbs+camps = im guessing main reason to even consider it
Culture alone is not a game changer, unless its static, so it kinda could mitigate some early boredom, but the only
benefit besize boredom is to get policies. You sacriface one policy, to get more policies faster overall.. I mean, that is the goal, but
do you really get that much culture? I dont think so..
Culture from barbs, can let you get faster second and third policy, since their cost is relatively low, but cost grow so much so fast,
that basically every policy later will be delayed.
Killing lowest barbs doesnt get you that much yields, and this will change a little about medieval, but medieval is just too late, its not exacly "early game".
Also to utilise this, you need army, and early army means lack of some essential buildings.
The way i see it, is that early game you want just bare minimum of army, because you need eko.
Also, killing barbs drain your HP, so you need to waste turns to heal, and that is why Endurance from authority is so synergistic.
Maybe you wouldnt need it if you done bunch of skirmishers, but they are only fast in open terrian without not too much rivers.
BONUS 2
You get +1 production = ok-ish, but not really a significant number
From one hand you get 1 production, but from other you delay +3 production from progress
So in this small window of early game, you might actually get less production, since even if you bee line to +3 production from progress,
You need third policy instead of second, not to mention, you would have to spend some additional production on units.
BONUS 3
You get bonus vs barbs = quality of life
Maybe that could have sense if you gone for "raging barbarians", there would be so much of them, that would be a significant bonus.
I saw few times, that barbs could conquer even some of AIs

But after tuning of barbarian spawning, normal, is just fine imo, and its kinda cheeting, since
player knows what will happen, and AI just react, so my guess is that AI response is not exacly correct to raging barbarians, but maybe this is only my "feel" of the game.
I did some small homework with InGameEditor and those are results
View attachment 685986
So over all, by the time you would normally got progress finisher, you would have to kill like 73 camps to break even, i mean obviously you woulnd need to kill barbs, but
considering, 3 barbs is equal to a camp, you would have to kill like 35-ish camps, and like 100 barbarians.. And in my personal experience, you would not be probably that lucky

If i recall correctly, Ancient and Classical camp culture are the same, and it increase in medieval to 50. So after some time its kinda getting easier, to get EXP but
as opener goes, i think you are delayed. Besize, you would have to be catching up whole game with the increased costs. Not sure if you would get away with that on Diety..
If my math is correct, the timings of 3rd and 4th policy should be similar. You waste one policy, but because costs are low, you are able to quickly catch up, but then the stairs starts.
Honestly, kinda same issue is with Fealty opener, you get monasteries, but you are delayed, so im doing of full Fealty or skip it.
Any way, its late and im tired, so if i did not took something into account, please correct me

Im curious of others opinions.