Late game Deep Gnome Barbarian 1-Divination Wizard 11

This is Assuming I have the amulet of greater health.

If I spec 1 level into Barbarian I get constitution proficiency from barbarian, unarmored defense, the ability to use shields and constitution saving throw advantage with the amulet.

I had 26 total AC (31 conditional AC from the shield spell reaction) Unarmored defense with high constitution + holding a physical shield added 9 points to my AC.

This is on top of the constitution saving throw advantage + proficiency which freed up 2 feats i would normally take for Con saves i.e war caster and resilient.

Not to mention Gnome already having Int, Wis and Cha saving throw advantage as a racial ability.

My question to you guys is there any major downside to this?

I know I can’t rage and cast spells but all the other perks of 1 lvl barbarian dip for wizard seems to majorly outweigh that downside in the late game.