GWM also works nicely with barbarians. Reckless Attack both lands blows when you have -5 and gives you crits more often so you get a bonus action weapon attack. This can work with half-ocr (above) but doesn't need to. Barbarians don't have a lot competing for their bonus action.
Polearm Mastery is a bit of a different beast. It's a consistent bonus action attack, which works well with rage giving you a melee bonus. But it means that you get minimal advantage from the crit/slay boost of GWM, so I wouldn't recommend both (at least not early on in adventuring).
I actually do recommend both for the following reason. That 1d4 damage bonus action attack becomes a lot better with the +10 from GWM which as you said combines well with reckless attack. PM (assuming using a reach weapon) also lets you get within 10 ft of a foe and attack them, then move 5ft beck without triggering an OA, then if the foe steps into your reach you get an attack. PM is such a solid way of getting 4 attacks in a round, and GWM lets you potentially at +10 damage to each of those attacks. I say get both early if you are trying for a Max damage.
That being said, I completely agree with the rest of your post.
Oh and a couple of things to add.
Dual wielding is great on a Barb until level 4-5 since it lets you potentially land more blows which equals more Rage damage, for example at level one assuming 16 Strength one Greatsword attack is 2d6+3+2 damage, but two handaxe attacks are 1d6+3+2 and 1d6+0+2. Once you have another source for more attacks this is less useful. I don't recommend it beyond level 5 especially if you pick up GWM or PM
Shield Master Barbarians can be great fun since Rage Adds advantage to shove checks and Danger Sense adds advantage to Dex saves.
My favorite Barbarians at level 6 would be.
Variant Human with GWM and PM.
Half Orc with either GWM or PM intending to pick up whichver one it doesn't have at level 8.
Goliath with Shield Master for a Tough Barb Stones Endurance adds a great use of a reaction on an already durable character.
Mountain Dwarf is also fine for any Barb build, Hill dwarf is Great for a defensive barb if you don't mind Starting a little behind in Strength.
I'm not up the races from Volo's guide, but I imagine bugbears work great, and Firbolg would be an interesting Bear Totem barb I think. It would start with a little lower Con, but a higher Wisdom and high Wis is great on any Character.