I've been toying with various approaches to making Two-Weapon Fighting interact better with other class features that use a bonus action. I am considering removing the bonus action requirement of Two-Weapon Fighting, either outright or as an addition to the Dual Wielder Feat. The additional attack is still limited to once per turn.
Does experience with this house rule reveal exploits or that it makes things unbalanced?
The single biggest limitation on PCs (or any creature) is the restriction imposed by the action economy, specifically:
In a combat, the side that can consistently make the better choices for the use of these limited opportunities to act will, all else being equal, win.
There should be pressure on a PC to struggle with if the Attack, Disengage, or Hide action is the best choice right now. Similarly, PCs should always be looking for ways to trigger a bonus action rather than not and making decisions about which bonus action is optimal.
With particular reference to two weapon fighting, there is an inherent trade off between making another attack versus using a more damaging weapon or getting extra protection from a shield: this doesn't change under your proposal. Notwithstanding, two weapon fighting is powerful - it doubles the potential damage output of low level martial characters and while it's utility lessens for characters that get extra attacks it is still a solid bonus action choice. Which is really the point: it should remain a choice - not something with no cost.
However, to consider just one potential abuse of your system: I will play a rogue who uses daggers (light finesse melee weapons that can be used for two-weapon fighting and trigger sneak attack). At second level I get cunning action - if I use the bonus action to hide I will get advantage on my first attack and trigger my sneak attack damage. Under the published rules I have to make a choice: hide and make one attack with advantage and sneak attack damage or make two attacks. Under your proposal I will always hide and make my first attack with advantage and sneak attack and get my second attack as well. A difficult choice becomes a no brainer and that is not a good thing.
For a STR-based character in tier 1 play (or otherwise without extra attack) with no damage bonuses, feats, or fighting style, this is already slightly better than wielding a greatsword:
The only real drawback would be weaker opportunity attacks, which can't be relied on to come up very often.
A bigger issue comes up with damage bonuses such as from barbarian rage or spells like Hunter's Mark, since those would now be applied twice per turn instead of only once.
It's also worth noting that the "two-weapon" fighting style provides a larger damage bonus than any other style, if you are two-weapon fighting every turn.
Once tier 2 is reached and STR-based characters gain the Extra Attack feature, it balances out a little more with greatsword builds having higher damage if not boosted in any way, but two-weapon fighting being able to achieve higher damage.
Another problem is DEX-based weapons, since DEX already offers many advantages over STR, allowing DEX characters to attack for 2d6+DEX damage as an action makes these builds much stronger.
Then there's features such as a rogue's sneak attack or a paladin's divine smite, which depend less on weapon damage and more on how often you hit - which makes two-weapon fighting more valuable.
TWF is currently niche, but not completely unused and often not terrible even when it is slightly sub-optimal. Buffing it across the board may make it "viable" in cases where it currently isn't but is likely to make it slightly OP in cases where it is currently slightly sub-optimal, and very OP in cases where it is currently viable.
