You will have at most a str stat of 16 for most of your career, that's +3 to hit compared to +4 or 5. That's a huge difference. Later you combine this with -5 to hit from GWF, that's just wont work.
If you use variant human for the feat at first, then your stats will be less since only +1 at first for racial. If you take variant human heavy armor mastery you can get +2 in strength at first level, but you want barbarian so that's off the table. It also means 15 at point buy in str and con, so a 14 and a 13 wont happen with a 27 point buy. You can get a 13 and 12 with 2 8's. Your ac will now be lower and you can't multiclass into a cleric unless you bump the score, which burns a feat. You could go with 15, 14, 13, 13 to cover the multi-classing requirements early.
You will have the lowest AC of the people on the front line so will be getting hit so counting on bless past the first round is assuming you will pass multiple concentration checks. Plus Bless is an action, so you give up a round of attacks in most cases unless you get a "prep" round. A cleric giving up an attack for a bless spell is in most cases a no-brainer, a fighter type giving up multiple attacks isn't.
With those feats your base stats never move. They will always be behind and be a constant drag. Your AC wont move either with no CON or DEX bumps. Bless (which cant be counted on round after round if you cast it and fight) and reckless attack wont cover this. Constant advantage is a reach, and you give up advantage to get it with the barbarian features.
The more I see this the more I am convinced this is a book build and not a build that has ever been played.
1. Okay, smack down time.
2. This is the build I took through HotDQ and then through RoT, all the way up to beating her. All AL legal rules, played as written and open rolling. Currently sitting at level 17 AL legal.
3. 17 AC is plenty to avoid hits by minions. I don't care about dodging hits from the BBEG, because someone has to eat them and I'd much rather it be me with my ~200 health, that de facto doubles when I'm raging. Please, again, tell me of these high level encounters where you are fighting enemies that are doing only B/P/S? Not Cones of Cold going off every other turn, Fire Balls, Walls of Fire, etc? Or, as in HotDQ, dragon breath weapons?
4. I don't care about the AC being low. If for some reason I did, I'd just cast Shield of Faith. But at higher levels (real AL legal play not whatever prior editions homebrew you're talking about), having more health = more important than AC. Why? Because waaaay more attacks trigger off of saves or the BBEG has +12 to hit so who cares? Minion to grant Help function for advantage and BBEG is good to go.
5. No, I lock down the BBEG away from in. You don't HAVE to use your PAM on the first enemy that enters your range. If you are, you're an idiot. That combo of feats, however, does guarantee that me and my huge pool of HP will be the center focus, which is exactly what I want.
6. I am 100% convinced you only play some homebrew with a cake walk DM if you think HAM is remotely worth it as a feat at any level past 5.