While the damage is similar on a very basic level there are some problematic points.
Very basically the damage output is similar.
You're spot-on here. The weapon damage is similar for one pair of dual wielding attacks to a single attack with a two-handed weapon.
Comparing a Greatsword to two Shortswords the damage is similar. With a +5 modifier we get 2d6+5 or 12 for the Greatsword and 1d6 + 1d4 + 4 or 10 for the two swords. Notice that you will make more crits with the two swords than with the one without increasing the damage output, since the Greatsword has better damage dice than the s6/d4 combination. However you decrease the standard deviation on the damage with favors the players. Note: With an even modifier the difference is only 1 rather than two.
Halving the modifiers is suspect
Adding half modifiers makes it more complicated to determine the damage. This can be fixed by noting on the character sheet the damages, like we do, e.g. for Jack of all trades. More problematically, you're at a disadvantage with certain modifiers. Normally, having odd ability scores is bad. Now it still is, but having an odd modifier also is. This means that the only score where you "lose nothing" is 18 (+4). Loss here means opportunity cost from ASIs (which is normal) and loss from rounding down - which is added and which is especially unfortunate if you have a 20. While you get a plus one on attack rolls with 20 compared to 18, your damage is the same.
What is the light restriction for?
I'm really wondering why you need the restriction to light weapons. Allowing d8 weapons would increase the damage by 1. This would mean that you are really even with the Greatsword when using at least one d8 weapon (and you have an even damage modifier). Also, this seems to help your 4th declared aim of enabling the use of a bigger and a smaller weapon.
There are interactions with on-hit and on-crit effects
While many on-hit effects only work once per turn or require resources (ki points, spell slots, a bonus action...) there are others that do not. Two examples are Hunter's Mark and bestow curse which deal extra damage on each attack no questions asked. There are other similar features which I will not list now. You have a similar effect with extra crit dice, which profit from the increased number of crits.
These features (which there are more of) scale directly with the number of attacks so they might be overpowered with the high number of attacks your design generates. Imagine you have three attacks per action and have bestowed a curse on an opponent to deal extra damage[1]:
With a two-handed weapon you get 3d8 extra damage.
With normal dual-wielsing you get 4d8 extra damage.
With your design you get 6d8 extra damage.
In conclusion, any per-attack feature without a cost or a once-per-turn restriction scales drastically with your design.
Many attacks take long to resolve
Resolving many attacks is time-consuming (Thanks to Ryan C. Thompson for pointing this out). Even if the overall combat time is not increased, the players not dual-wielding need to wait longer for their turns because which can feel bad potentially.
[1] You cannot do this as a normal fighter but you can do it if you multiclass and there are probably similar features which you can get more easily.