But two-weapon fighting does take a bonus action. So if you Action Surge, you can attack twice with your main weapon but only once with the off-hand; unlike single-weapon fighters, you don't get two full sets of attacks out of it.
Exactly, yes. So with the book rules whey you use Action Surge you can take an extra Attack Action and get all your attacks with your main weapon, but you don't get an extra bonus action, so you can't make a second attack with your off-hand weapon. With my proposed change, every time you take the attack action you get one attack with your off-hand weapon, so you would get a second attack with your off-hand weapon.
Note: This wouldn't help you if you had Haste cast on you, as it specifically says you can only make one attack if you use the Attack Action. So once again the Great Weapon Fighter has an advantage.