No. By that logic you couldn't have a leader (Just look at Axe in Dota 2. He's the "leader" of an army because he killed his way up the ranks to show he was the strongest. He proved he was, but there was no one left to lead because he **killed everyone**).
Even if strength is a factor (and for the sake of argument, we will say it is a factor for barbarian leaders) in leadership, you need more than just strength to be a leader.
Most important thing you need is charisma. You need to get people on your side, to fight for you and possibly die for you. Sometimes it's not you that needs the charisma, but your goal.
Let's take a look at King Obould Many-Arrows from the legend of Drizzt. He's an orc barbarian warlord who is introduced by kicking the ever loving crap out of Wulfgar (you could argue the Worf effect). But he's not your average orc warlord who is content in keeping his position. No, he has a dream of creating his own kingdom for orcs.
And he did it. He made that damn kingdom, not just because he was strong. Thousands of orcs are strong, strength is a big thing in their culture. Obould however was intelligent, even by human standards (honestly a lot of characters in Drizzt seem to be special for some reason) and was able to create peace treaties with "goodie races", even traded with them.
Now his strength was important, but if that was all he had then he'd just be another warlord among orcs.
Why am I talking about this? Well this relates a little to Sejuani. I've heard people argue that she is supposed to lead by charging headfirst, by being the strongest.
That's not why Sejuani leads. She's leading because she has a vision, the determination to see it happen, and the charisma to get people to follow her. Strength is important, but she isn't the strongest person in the Winter's Claw. I'd argue that's Olaf because he is fated to not die in battle, and he only follows her to find a death in battle.
Idk. I just never saw Sejuani as "I lead because I am the best!" I mean it is a factor since she doesn't take weaklings, but I don't think people only follow her because she's strong. They follow her because they believe in her vision and will fight to make it happen. Hell her E stacking on melee hits from allies shows this! They will fight by her side, empowering her to lock down an enemy and bring them down faster for the Winters Claw.
Sorry for the ramble. This just bothered me.