The difference here - and it's not a small one - is that it's not a dial. It's a switch, swinging between the two extremes.
I disagree. The switch implies a dial and, frankly, I think most play will be somewhere in the middle.
If you build it into the math with something like inherent bonuses, you can preserve the "interesting stuff" feature of magic items without paying much attention to the math on the player and DM sides.
I wouldn't have a problem with magic items
not providing bonuses at all, but I'd very much prefer not to be
required to include inherent bonuses just to make the math "right."
If you have bounded accuracy and you're not paying attention to even the minutest changes in d20 rolls, it's simply not good design.
Again, I disagree. As long as the DM is advised to keep in mind that magic items make characters more effective, things should work out just fine. Bounded accuracy allows a DM to pay less attention to the math because the difference between "more effective" and "less effective" is never so great that it breaks the game. I get the feeling you think that allowing the DM to pay less attention to the math is a bug. I view it as a feature.
OTOH, if magic items are mostly good for some extra damage and effects, or small amounts of DR, it's more sensible. We've established that damage isn't bounded to the same degree as d20 rolls.
I would not have a problem with this at all.
But that's not what will happen. Barbarians aren't prevented from wearing armor, and given that light armor has no downsides, it's sensible to wear it as soon as it's better than iron skin. It's a helpful perk at low levels, for sure, but at worst, a barbarian is keeping pace.
It's probably worth noting that the barbarian is proficient in only light and medium armors (and the shield, of course).
Thus, the highest AC a barbarian can have with +1 armor (without using a shield)--assuming a Dex bonus of less than +5, which is probably a safe assumption for most barbarians, but is also irrelevant to the comparison between no armor and light armor-wearing barbarians--is AC 18--and that's while wearing expensive dragon scale or very expensive mithril armor.
Furthermore, the dragon scale armor makes stealth (and, consequently, ambushing) very difficult, which is something that an unarmored barbarian with high Dex should be able to do pretty well.
All in all, the trade-offs seem pretty balanced to me.