Just a quick note. My comparison involved taking the feat in lieu of an Ability Score Increase, which affected how fast the character reached their maximum strength score.
I suppose I could compare to GWM, but that is one of only two or three feats that I do feel is overpowered. Plus, the bonus action trade-off is an important point of comparison, which GWM mostly misses.
I realize this a discussion about balance, so feeling something is overpowered is not off-limits, but it does strike me as funny that you feel GWM is OP, while not Polearm Mastery. Also GWM is better in the hands of Berserker than Polearm Mastery is (this could be debated), so GWM needs to be in the discussion if we are talking about balance.
When I was making a fighter, I wanted to really get a sense for weapon balance, in this process I had to look at feats involved with each weapon choice. The feats that I looked at, were GWM, Shield Master, Polearm Master, and Dual Wielder. I also considered a combination of GWM and Polearm Master. I ran average outgoing damage and incoming damage, based on my group makeup (melee rogue and paly with GW). At lvls 5 and 10 (and just a little at 20) with both advantage and no advantage, and also burst rounds vs non burst rounds. My conclusion was that GWF and Polearm Master were very good, but definitely in the same ballpark with sword and shield with Shield Master. The reason this is relevant, is that in my numbers the real equalizer is not Polearm Master, it is GWM. I realize that you find it OP, but it is this feat that makes the Berserker on par with the Totem Warrior. Any discussion about balance between these 2 paths needs to look at GWM.
S'mon that is a very nice set up, and very damaging. Depending on the situation it can be more or less damage than taking a +2 Str instead of Polearm Master. The real bonus is in attacking from 10ft and then taking an Op attack if they engage. This will negate the advantage given Reckless Attack, but also it takes you out melee contact with the enemy and does make you less of a tank for the party (if tanking was was your point). Sentinel could also be used instead to help keep the focus on you.
If we keep GWM as the focus, then Berserker gives a viable alternative to Polearm Master (even though a Berserker could very easily pick this up as well, just they do get a little less out of it than a Totem Warrior). The real strengths of the Berserker imo, are Mindless Rage (mostly because it is reactive and stops the the most nasty effects on a melee class, fear and charm (dominate is a charm effect btw), and Retaliation (I know it is lvl 14, but it is sooo good).
Another point to consider in DnD is that not all fights are as important. While the player might not know which is and which isn't. There are many times when it is obvious and the players know when the big fight is. In 4e this is when the players would blow all their action points and daily powers. While the days of action points and dailies are mostly gone, the Barbarian does shine in this situation, especially the Berserker. With Frenzy and GWM the Berserker is a better burst damager than the Totem Warrior. So when it really matters, the Berserker is doing more damage.