I wonder if dual wielding would be better if you would separate it from Bonus Action entirely. Give a free off-hand attack but also a -2 attack penalty for both hands, like in previous editions.
I would also experiment with giving an extra off-hand attack with extra attack and see if that -2 would be enough to keep it in check. The power builds would be a big problem though.
Oh boy you're going to make me do more math to measure the effects on DPR of this -2 to-hit, aren't you? :P
Leve 4 Fighters in this new "-2 to hit dual wielding" system
-Sword and Board who increased Str+2: ------ 1d8+6 MH, AC 18 - DPR = 7.4 (70% to hit)
-Greatsworder who took and uses GWM: ----- 2d6+14 MH at a -5 to-hit, AC 16 - DPR = 8.4 (+1.4)
-Dual Wielder Feat with two longswords: ---- 1d8+3 MH, 1d8+3 Off-H, AC 17 - DPR = 8.25 (only 55% to hit, but no BA cost)
-NO Dual Wielder Feat with two shortswords: 1d6+4 MH, 1d6+4 Off-H, AC 16 - DPR = 9 (only 60% to hit, no BA cost)
We still see that 1 less AC converts to ~1 DPR. But now Dual Wielders have a free bonus action!
Perfectly BalancedLeve 5 Fighters in this new "-2 to hit dual wielding" system
-Sword and Board who increased Str+2: ------ 1d8+6 MH x2, AC 18 - DPR = 14.7
-Greatsworder who took and uses GWM: ----- 2d6+14 MH x2 at a -5 to-hit, AC 16 - DPR = 16.8 (+2.1)
-Dual Wielder Feat with two longswords: ---- 1d8+3 MH x2, 1d8+3 Off-H, AC 17 - DPR = 12.4 (only 55% to hit, no BA cost)
-NO Dual Wielder Feat with two shortswords: 1d6+4 MH x2, 1d6+4 Off-H, AC 16 - DPR = 13.5 (only 60% to hit, no BA cost)
-Longsword Dual Wielder + extra off-hand att: 1d8+3 MH x2, 1d8+3 Off-H x2, AC 17 - DPR = 16.5 (only 55% to hit, no BA cost)
-Shortsword Dual Wielder+ extra off-hand att: 1d6+4 MH x2, 1d6+4 Off-H x2, AC 16 - DPR = 18 (only 60% to hit, no BA cost)
Sword&Boarder deals more DPR and has higher AC than the Dual Wielder, regardless of whether the feat is taken or STR is increased.
To recover the "1 less AC converts to ~1 DPR" trend, both variations of the dual wielder need +3-5 DPR (or +2 AC) for levels 5-10. Your solution to give the extra off-hand attack works ~perfectly.
I presume that 5e turned this free off-hand attack into a bonus action for the same reason as most of its design decisions - to simplify things especially combat. They didn't want numerical penalties to rolls, and ^ also limits the # of actions someone can take in a turn. But as I oft repeat, since BG3 is a videogame that automatically performs all calculations, it can and should add back in some complexity.
