Hiya!
What about looking at it from the other side...a barbarian is a "berzerker", as per the old skool style of 'monster'. A dude that is constantly in a state of intense anger and violence. The only way for them to feel 'calm' is to start killing stuff and fighting; the "fight or flight" effect actually gives these poor souls something to focus on, allowing them, for just a few moments (the duration of the fight) to ignore all the 'mindless rage' bombarding their brains.
So... a "Barbarian" (in 5e terms), is a special person born (typically) to a barbarian tribe. These people (like albino's, or being born with a specific physical characteristic that isn't normal for your race, etc) are immediately trained to control their Rage. To control the "Sprit of Talzaar", or the "Soul of the Wolvereen", (or whatever you want to flavour it as for your campaign). Without this training, they would become near mindless killing machines, doomed to die a quick death. Some who are born with 'the mark' don't develop the Rage until later in life, usually after a traumatic event, but if you are born with 'the mark', you will loose control. When you do, without training, you become a "berzerker" and will die shortly there after (if not by violence, by stress on the body...usually within a few months to a year).
How about something like that? That would mean that a higher level barbarian has learned to control this better so that he can 'let it free' more often than others and not risk loosing control and becoming an NPC. This is sort of (mechanically) how I do 'rage barbarians'. I also added in that once a Barbarian enters Rage, he has to make a Wisdom save to come out of it (he can get bonuses from others helping him...dangerous though). If he fails to make his Save by a number of rounds after his rage 'ends', he becomes a berzerker NPC. After his rage ends, however, he is still 'raging' (e.g., he effectively has 2x the number listed in the PHB)...but any target, foe, animal or friend, is subject to attack). It's been the death of at least two other players characters, and one dwarven barbarian became "NPC status". Harsh, yes, but IMHO Rage is pretty freaking tough! (at least it was in 3.x/PF). With 5e, not quite so bad...but still rather powerful.
^_^
Paul L. Ming