The Issue
So, it is well known that the Dual Wielder feat is bad. Even if you are building a Two-Weapon Fighting character, the feat is still worse than simply getting straight-forward ASI. Unlike Polearm Master which is a go-to for someone using a Polearm, or Crossbow Expert for someone using a Crossbow, or GWM/Sharpshooter as good increase in DPR against low-AC enemies, plus some nice utilities (extra attack with bonus action, or almost-infinite range), the Dual Wielder is the last thing you are getting as a Two-Weapon Fighter (although you are probably still getting it, at least).
Furthermore, the Dual Wielder feat as is, for me, is boring. If I am playing a dual wielder I probably want to be dealing lots of damage, not have a +1 AC. And finally, Dual Wielder pretty much assumes Two Weapon Fighting, which is known to be subpar as Extra Attacks get into the game, since the benefits of +1 attack get diminished when you are already able to make 3 attacks anyway.
To summarize, the issue I have is:
Two weapon fighting is already subpar.
The feat that should make this style more viable is near useless.
The Proposal
With that in mind, I decided to change the Dual Wielder feat for something more in line with the glass canon damage dealer I have in mind.
Dual Wielder
Prerequisite: Two-weapon fighting (Fighting Style)
When you take the Attack action and attack exclusively with a light melee weapon that you’re holding in one hand (i.e., all attacks are made with the same light melee weapon, with the same hand), you can use a bonus action to take another Attack action in order to attack with a different light melee weapon that you’re holding in the other hand (again, all attacks should be made with the other weapon and other hand, respective to the previous attacks). If you do so, Attack Rolls against you have advantage until your next turn.
So, the idea here is that now, if you have Extra Attack, your bonus action actually can use them.
Comparisons
As baselines, I have used the following Pure Fighter builds:
Greatsword, Great Weapon Fighting and +1 ASI.
Greatsword, Great Weapon Fighting and Great Weapon Master.
Two-weapon Fighting, +1 ASI.
After getting the feat, all levels are +ASI.
Obviously, at 4th level, TWF with +1 ASI is better (since you don't get extra attacks yet), as well as the GS+GWM. At 5th level, it is still worse than GS + ASI for all ACs.
At 6th level, it starts getting interesting as we get +ASI in our primary attribute and that is used in each of our attacks. However, GS + GWM still outdamages this feat for low ACS (AC <= 13), GS + ASI outdamages for high ACs (AC >= 19), and the feat is the best option for mid-range ACs (13 <= AC <= 19). Note that this still comes at the cost of being vulnerable to enemy attacks with advantage. An example figure for better visualization.
At 8th level, we get a +5 modifier in our main attribute and the feat starts to shine. It can only be outdamaged by GS + GWM for low ACs (<= 11), and shines for anything higher than that.
As we get higher proficiency bonuses and GWM starts to hit more often at higher ACs, GWM comes back against enemies up to 14 AC, however, the new feat still shines against high ACs - which are arguably more common at higher levels.
Trade-offs and concerns
So, basically, the feat gives a good damage potential (from my point-of-view), at the cost of being vulnerable. My concerns are:
I can see this being quite overpowered for a Fighter 17/Barbarian 2, exploiting the Rage Damage for +2*8 extra damage and Reckless Attack basically giving advantage with no cost, as the enemies are already getting advantage in their attacks anyway. One way to solve this is simply not allowing both features to be used.
I am not sure how this will impact Rangers with Hunter's Mark. Rangers are quite bad in 5e in my opinion, but this could be a game changer for them. Would they get too strong?
Is simply giving advantage to attacks made from enemies enough to compensate for the considerable damage potential?
On the other hand, is this as good as it seems? Are my baselines good baselines, or am I using subpar damage dealers anyway and outdamaging them is no big deal?
Additionally, there are a few trade-offs that are not obvious on how to evaluate and depend on the campaign:
Getting one magic weapon is easier than getting two magic weapons.
Forcing 8 Concentration saving throws is better than forcing 4 concentration saving throws.
Having your bonus action for something else is better than not having your bonus action for something else (although it's hard for me to figure out what would be better than using it to considerably increase your damage).
So, for example, if we take into account a +3 Magic Weapon at 20th level, the GS + GWM build outdamages the new feat up to 20 AC, and loses by less than 10% above that, without costing the bonus action and without costing advantage for the enemies.
So, for now, I think this is decently balanced, but am I missing something? This is a very simple change and I would assume someone has already tried it out, if this is the case, I would love to get an answer from actually testing it.
In the case it is overpowered, is there some way to balance it through making it "cost" more, but maintaining the idea of attacking twice the number of usual attacks?
If it is underpowered... Well, then dual wielding seems to have no hope other than for flavor haha.