Using a longsword instead of a greatsword is already an opportunity cost. Heck, using a longsword instead of a rapier is already an opportunity cost. You chose a class that gives more freedom in how you build them, and you used that freedom to take many defensive options when you could have taken options that provide more damage and more versatility (such as being able to still use a bow pretty well by choosing dex). It's an opportunity cost.
My argument with AC wasn't that "saving throws exist", but that you should also take a look at cases where you're taking attacks at advantage, because that's more favorable to the barbarian. Also that bad luck happens, crits sometimes happen in quick succession, but a barbarian's form of tankiness is more effective at dealing with that.
But beyond that, as I've already said in my other comment, the fact that a barbarian's defense isn't so much tied up in AC means they can still use a two-handed weapon and do more damage while retaining more defensive power then a fighter would have if they chose to give up a shield. And looking through the anydice chart, with barbarian AC being put as 17...so you were already comparing a barbarian using a two handed weapon against a fighter with a shield? And the barbarian was still able to take a good deal more damage?
As for rages, yeah, it's a serious downside, but one that matters on a more longer term scale. Taking a bit of extra damage in encounters not worth raging in is a problem, but one that can be solved with health potions, healing spells, and short rests. That's a cost, but what the cost pays for is having rage up for difficult fights to keep you alive...and if you don't survive the difficult fight, the macro-level management of hp wasn't going to matter anyway.