In calculating the damage done over an adventuring day, you also really have to consider the value of the damage being done. In this sort of case, spike damage is worth a lot more than consistent damage, since the ability to take out an enemy in one or two rounds is a huge force multiplier and can end up reducing the length of combat over an adventuring day considerably. Yes, a Barbarian will do more damage over the course of a longer period of time, but it completely lacks in any way to front load a lot of damage in a single crucial instance (remember, a Berserker can't benefit from the effect of Frenzy until the turn AFTER it is activated, since entering rage takes up a bonus action), outside of multiclassing (which does come with its own compromises). With that in mind, it should be doing more damage over drawn out periods.
Also note that most of these frontline classes provide their damage with additional utility, which the Berserker does not really provide. Even Totem Warrior, with its own selection of potent support abilities, approaches (and in some cases, at lower levels, even surpasses) Berserker damage rates at higher levels, thanks to the new tiger totemic attunement.