I can’t imagine too many scenarios where allowing someone who is wielding a one-handed (or versatile) weapon and nothing in the off hand to have a bonus action unarmed strike to be game-breaking. Seems like an easy call to me.

So there’s a few issues here:

• Unarmed Strikes do not require an open hand. Punches, kicks, and slams all count as the same Unarmed Strike
• If you were to allow this, there would be no reason to allow someone with two Shortswords or a Greataxe to do a BA strike
• …which would then render the BA attack from Polearm Master moot since they no longer need a feat to do that
• I’ll also note that the fighter with a sword in one hand and nothing in the other is likely using the Duelist fighting style, so that sword attack is effectively two die sizes larger. A Duelist Longsword is roughly equivalent to a Greatsword to put it in perspective

At the end of the day, allowing martials to perform a BA Unarmed Strike wouldn’t be game breaking, but it needs to be applied universally which has secondary implications

You need to be trained in some sort of unarmed fighting style to be able to throw a kick in between slashes. If you did it untrained, it would leave you unbalanced and prone to get hit.

Makes sense to let a monk with a quarterstaff do it and not a barb with a great axe.

Instead of using a weapon to make a melee attack, you can use a punch, kick, headbutt, or similar forceful blow. In game terms, this is an Unarmed Strike

D&D isn’t a real world simulator. It values them all equally.

You technically can’t do an unarmed strike if you have a 2hander. Quarterstaves are versatile weapons, which allow for monks to do kicks while using them.

I know what you said, but the mechanics still don’t allow for kicks with a regular 2hander. I was trying to rationalise the actual mechanics with some real world logic.

Do you know where it says you can’t unarmed strike while holding a two handed weapon? I’m not seeing a requirement for a free hand in the rules.