Cap'n Kobold
Hero
Part of it might be due to unarmed strike being considered an attack with the body overall, (which could include kicking, headbutting etc) so the concept of an off-hand attack just isn't relevant, rather than a specific fist (which would imply the ability to attack with the other fist as you say.)
Since Unarmed strike isn't reliant on having a hand free, there would need to be some justification for why everyone doesn't always get that extra attack in combat.
I'm generally OK with the rules as they are: I view trying to attack an armed opponent with an unarmed attack is hard enough that there are less openings available despite the number of body parts you are bringing to bear. I'd probably allow someone with the TWF feat to make an additional unarmed strike as a bonus action perhaps.
Remember that PCs are assumed to be individuals with a broad range of capabilities and skills. They know how to punch just as they know how to throw a knife, which is also a fairly rare skill.
Since Unarmed strike isn't reliant on having a hand free, there would need to be some justification for why everyone doesn't always get that extra attack in combat.
I'm generally OK with the rules as they are: I view trying to attack an armed opponent with an unarmed attack is hard enough that there are less openings available despite the number of body parts you are bringing to bear. I'd probably allow someone with the TWF feat to make an additional unarmed strike as a bonus action perhaps.
Remember that PCs are assumed to be individuals with a broad range of capabilities and skills. They know how to punch just as they know how to throw a knife, which is also a fairly rare skill.