You mean, like an Avenger?
I think, looking at the attributes, a Barbarian that's not investing in Dex (or Int) -should- upgrade to heavy armor (particularly a Rageblood) by Paragon levels.
A better alternative (from
Dungeons & Dragons Roleplaying Game Official Home Page - Article (Excerpts: Primal Power Feats) ) for Rageblood barbarians is the upcoming Hide Armor Expertise -- which lets any Primal with at least a 15 Con and Hide prof. character use Con instead of Dex/Int when wearing hide.
Thaneborn, OTOH, are probably best starting with a 12 con, and letting it upgrade to 13 and grabbing Chain (and probably Scale) proficiency (or maybe even starting with a 13 con and figuring on getting plate and plate spec by epic levels).
Because, well, yes, you can take a few hits against AC at heroic levels. But as it is, you lose a point (of overall defenses) at paragon, and another point at epic, on top of your frontloaded points (and fundamentally, the AC points are more valuable. Who cares if you've got a bit more resilience against Reflex attacks than average when functionally, both your AC and your Reflex are terrible?)
It does look like they're making a good show at fixing the bear shaman and thaneborn barbarian, who downright resilient if you let them use con->AC with one feat.