I like this approach, but it's still a matter of deciding what "balanced" means. As others have pointed out, as a rule of thumb/on average, dealing more damage is better than an AC bump. So high does an AC bump or other defense have to be before that's balanced? Ask five people in this thread, you'll get seven different answers.
Well, for "balanced" we need a couple of criteria, and that's beyond just number crunching dpr on both the giving and taking sides.
1) There needs to be distinct niches. If you give everyone the power attack boon, suddenly, all styles play alike. This is bad, because then we'll have objectively better/worse choices, with only tiny variations. You'll have one style 100% overshadowing another, and that is flat out bad all the time.
2) Needs to make thematic sense. While some people are happy with any numbers, the vast majority of players want something that makes you feel like duel wielding, or really using your shield in battle, or that you are using spear tactics in battle. Hitting hard with a giant weapon makes sense. Hitting hard with a dagger? Not so much. Now, hitting with a flurry of thrown daggers which happen to deal a comparable amount of damage? That's another matter.
3) Needs to be active and engage the player. Polearm mastery lets you make off turn attacks, and bonus action attacks. Great Weapon Mastery lets you decide to power attack on a turn by turn basis, and it gives you Cleaves if you kill an enemy. Duel Wielding gives you static bonuses. The former are far more engaging on the table than the latter. As well, we don't need feats to give static bonuses - that's what the option to raise your attribute is for.
4) The numbers should roughly equal out, and not vastly overshadow the other. While optimizers and power gamers may consider one thing or another "superior" to another, a lot of the overall impact on an actual game isn't noticeable, since GM style plays a huge part. Great Weapons, Polearms, and Shields are all roughly equal, though they all play differently; heck, Shield Mastery is primarily defensive, and that's super attractive. For that matter, grappling and unarmed strikes work well through their feats. They all work differently, they all are roughly equal, making each a stylistic choice.
Defensive Duelist and Duel Wielder, however, has no such luck. They're too far outside the benefits of the others. The standard is +2 of your main attribute. The good feats are slightly better than that, but in niche situations. The bad feats are objectively worse than it in their situations.
I mean, is Shield Master balanced with GWM? I think so. I think the combat options it offers, when combined with the defensive bonuses, make it equally attractive (depending on character concept, of course). But others don't agree. Is Dual-Wielder? Well... Probably not, no. Adding a second off-hand attack might not seem like much--look at the monk--but it has some repercussions. Rogues suddenly have yet another shot at SA damage. And combined with the "can use non-light weapons" benefit, it starts to look a little broken.
You mean like giving Power Attack in a game where AC doesn't grow, but weapon accuracy naturally does? Repercussions like that?
The non-light weapons thing is actually really negligable. The only non-light weapons you can really use one handed (and thus with the feat) are the rapier, morningstar, and longsword; d8 weapons are your only choice, as all d10 weapons and above are two-handed. That's an average of +1 damage increase a hit. While not -nothing-, its not exactly something to write home about either. That +1 is hardly going to make anything broken.
The multiple attacks with something akin to Hunter Marks/Hexes, Two Weapon Fighting Style, and the kin is where I'm leery. Another attack could end up mathematically breaking the game, especially at lower levels. It also steps on the Fighter's toes of being the one with so many attacks. Could look into making it not take a bonus action, or increasing damage dice, or other things like that. "Each time you hit during your Attack action, you hit with your offhand weapon as well. Do not add your STR/DEX to the extra damage, or any outside things like Hex, but yes to weapon dice and enhancement bonus. Use the lower of the two dice pools when making the attack roll." Poor wording, admittedly, but you get the idea.