I think it is important to consider why you are making this change.
If you feel that fighting with two weapons isn't offensively powerful enough, despite the added versatility of being able to use two different weapons and make melee or ranged attacks in the same round, as well as getting two opportunities to hit and apply special effects like sneak attack, and getting two chances to score a critical hit - then this rule change might be suitable as it makes fighting with two weapons more powerful.
If you are thinking of a different reason for the change, then my thoughts depend upon that reason.
As several posters have clarified, it is because bonus action conflicts make two-weapon fighting a substandard choice for the optimally minded player.
The path to dealing lots of damage (arguably the fundamental part of being a martial character in the first place) is to utilize
all your actions all the time, including a bonus action and (for the heavy duty minmaxer) the reaction.
This means that your baseline damage should, nay needs to, come about without taking either of those two.
If you use any other fighting style (greatweapon etc) you leave your bonus action open for being used for extra damage. This is the first step to an optimized character, that is, a character that can be as well rounded and as well characterized as any other; it just deals more damage, and is therefore better at its job.
Now, two weapon fighters need to use their bonus action each round to simply reach their baseline damage. Hence two weapon fighting style does not allow optimization to the same degree.
Which is exactly what the proposed change fixes.
(That does not necessarily mean the change is balanced or that I endorse it. The above is merely explaining why somebody would want to make the change)
Cheers,
Zapp
PS. This is also why the Barbarian Berserker is a poor choice (in games with Greatweapon Master feats), the exhaustion notwithstanding: again you have a basic build reliant on a resource best spared for optimized build choices.
In short: assuming every character build is equal, choose one that isn't based upon bonus actions. Because that lets you climb above those choices by using the bonus action.