SO. MUCH. HATE. Plenty for everyone!
Story wise and mechanically he was a fighter/ranger and the dual wielding came from his fighter background. Most people just see that he's a ranger now so rangers should dual wield.
Yup, I'd agree with this. Whereas most standard dual-wielding would be with two 1d6 weapons (shortswords / scimitars etc)... allowing instead a 1d8 / 1d4 combo is not going to cause that much difficulty or any tremendous unbalancing in my personal opinion. Damage is going to end up being close to the same in the end, so I don't see any reason to disallow it if the player wants to go rapier/main gauche for flavor reasons.
Yes the damage will be slightly better, because you can use just the 1d8 when you don't use your bonus action. That's how much the average 1H weapon deals, so no big change (you save some interactions of dropping/drawing weapons). The major change is when you add Additional Attacks, but as I mentioned earlier, that's when TWF tends to fall off the damage chart. This helps keep them in the mix.The 1d8/1d4 combo is a little better than 1d6/1d6 because on turns where you use your bonus action for something other than off-hand attacks you still get most of your damage.