I think the problem of the OP is much similar of the first version of the barbarian. Do we really want a class who has a such obvious choice as a feat? And an armor feat. It would be like a Crossbowman class, who could be doing more damage without any penalty by getting the longbow feat in the 1st level.
There should be always an OPTION to get a better armor, but likely not an automatic one, like the old barbarian and the avenger.
Wizard, sorcerer, and avenger all have an obvious choice of armor feat. And I haven't seen magical cloth armor that's awesome enough for me to want to skip leather prof.
And I think the OP's original reasoning might be a bit off, or I didn't understand him.
Barbarians in light armor have the same AC gap from, say, rogues, throughout all levels basically. +1 per tier meets the stat bonuses at 4, 8, 14, 18, 24, 28. Both characters get bonuses at 11 and 21.
if dex represents starting dex mod (with starting score even), then
Barbarian in hide at level 10, ac is 10 + hide + dex + 1
Rogue in leather at level 10, ac is 10 + leather + dex +1
Barbarian in hide at level 20, ac is 10 + hide + dex + 2
Rogue in leather at level 20, ac is 10 + leather + dex +2
Barbarian in hide at level 30, ac is 10 + hide + dex +4
Rogue in leather at level 30, ac is 10 +leather + dex + 4
In epic tier, the bonuses from 11 and 21 have kicked in for both classes. If the barbarian starts at 14 dex, and the rogue starts at 18, and neither improve ac by taking feats (of which there are far more available to the rogue (hide prof, two weapon defense, defensive weapon prof), which is my complaint) then the barbarian's AC is 1 behind the rogue's at the end of each tier. At the beginning of heroic and epic tiers, they're actually tied.