Martials don't even get anything from a 5th level multiclass into another martial class
(ttrpg.network)
The reason that it's broken (in a bad way) as Dex+Con compared to the Monk's Dex+Wis unarmored defense is that monks absolutely CAN get broken as fuck AC from Dex + Wis, especially as the game goes on. Kinda on a related note, in BG3 I re-specified Astarion as a thief/monk, gave him a few mid-tier magic items, and now he's my front-line tank with an AC of 21 at level 7. No sane Barbarian PC is going dex barb, so realistically the barbarian's unarmored defense is going to cap out at AC 15-16 minus shield (which, come on, what barbarian won't be rocking two handed weapons?). So, while the Monk gets unarmored defense based on both of its chief stats, Barbarian gets unarmored defense based on just one of its chief stats.
Having a barbarian with a broken AC to start with doesn't bother me too much, but then I also tend to not run gritty/from dark style games, and that's also bearing in mind that the martial classes don't really scale as well as the casters do after level five. Giving the barbarian a ludicrous AC to aspire to at high levels might help balance that out.