I again think people are missing the key element of two-weapon fighting, but you guys tell me if I am getting this wrong. At 5th level when you get a second attack as (for example) a fighter, you're attacking FOUR TIMES, and that's without action surge. This is from the combo of: fighting style, nick property, and two weapon fighting feat.
1. Attack with a light weapon. This gets your normal Ability score mod to damage.
2. Attack with nick, other light weapon, as part of attack action due to feat. Ability score mod to damage due to fighting style.
3. 2nd attack with light weapon, due to 5th level extra attack ability. This gets your normal Ability score mod to damage.
4. Bonus action attack with with dual-wielder feat (note: this language is not a replacement for the light property attack as written - clarified by Crawford). This gets your ability score mod to damage due to fighting style, and can be with a non-light weapon provided it lacks the two-weapon property. Thanks to weapon swapping, you can now stow and draw one of your light weapons to make this happen.
Here are all the relevant rules:
Fighting Style: Two-Weapon Fighting: When you make
an extra attack as a result of using a weapon that has the
Light property, you can add your ability modifier to the damage of that attack if you aren’t already adding it to the damage.
Weapon Property, Light: When you take the
Attack action on your turn and attack with a Light weapon, you can make one extra attack as a Bonus Action later on the same turn. That extra attack must be made with a different Light weapon, and you don’t add your ability modifier to the extra attack’s damage unless that modifier is negative. For example, you can attack with a
Shortsword in one hand and a
Dagger in the other using the
Attack action and a Bonus Action, but you don’t add your Strength or Dexterity modifier to the damage roll of the Bonus Action unless that modifier is negative.
Weapon Mastery, Nick: When you make
the extra attack of the
Light property, you can make it as part of the
Attack action instead of as a Bonus Action. You can make this extra attack only once per turn.
Dual Wielder feat: When you take the
Attack action on your turn and attack with a weapon that has the
Light property, you can make one extra attack as
a Bonus Action later on the same turn with a different weapon, which must be a Melee weapon that lacks the
Two-Handed property. You don’t add your ability modifier to the extra attack’s damage unless that modifier is negative.
I've left out of this other weapon properties but they can still apply. For example, think this is right (again tell me where I am wrong):
Lvl 5 Fighter with two weapon fighting, dual wielder feat, and 2 light weapons one vex (hand axe), one nick (scimitar?).
-Fighter uses attack action with main hand, triggering vex and nick. Offhand nick weapon attacks at advantage. Extra attack with mainhand after nick weapon attack, triggering vex again.
-Since I used the attack action I can still use bonus action to attack so now I get advantage again because vex is not once per turn like nick is
-End State: 2 main hand attacks, 2 offhand attacks at advantage. All with bonus damage from two weapon fighting.
As for Dual Wielder Feat working independent of Nick in this way granting a bonus action attack separately apparently Monte from Dungeon Dudes spoke with Jeremy Crawford at GenCon about this interaction and got verification it is intended to work this way. Here is a video covering why you get 4 attacks at level 5:
I do think, if this is right, that dual weapons outperforms single weapons up to around level 10 or 11, except when considering burst damage from limited resources.