The genesis of this question is that I'm looking to come up with a few default bonus actions anyone can use.
Normally if you fight with a light melee weapon in your main hand and spend your action to Attack, you can then spend a bonus action to get one more attack with a different light off-hand weapon, though you don't get to add your ability modifier to the damage (unless it's negative).
A typical light weapon does d6 damage (average 3.5), while a typical non-light one-handed weapon does d8 damage (average 4.5).
So I suppose the game is saying that if you're willing to sacrifice 1 point of damage per attack with your primary weapon (d6 instead of d8), then getting one extra bonus action attack that probably 3 damage is also balanced. That's a net of 2 damage.
(I know there's all sorts of other reasons you want extra attacks, like if you want more chances to land sneak attack, or if you spend feats or have fighting styles to improve it. But for a normal adventurer, an off hand attack as a bonus action nets an average of 2 damage.)
Anyway, if Attack is an action, and casting a spell is an action, would it be balanced to let a wizard cast a spell, then make an attack with a dagger as a bonus action (doing an average of 2 damage)? Or what if a character Dashes as an action? Would a bonus action attack with a club be fair then?
Heck, since anyone could have a free hand and just punch (doing 1 damage), is there a reason there isn't just a default option like:
Light Attack
Spend a bonus action to make an attack. If the attack hits, instead of rolling for damage and adding bonuses from ability modifiers, you just deal 1 damage if you are unarmed or only have one weapon, perhaps by delivering a pommel strike or a tiny slice. However, if you make this bonus action attack with a weapon that you aren't using for other attacks this turn, it does 2 damage instead.
I am not really a fan. The cool thing about bonus actions is you have to build a character that has those options. It is special, making a bonus action available to every character every turn would make those things less special IMO.
Also this will slow down combat as every character and every monster that uses a weapon would do it every turn if they did not have another BA option.
In terms of balance there are six problems I see. Most are not gamebreaking but they will upset or substantially alter the game I think:
1. It changes the balance of monsters. Goblins would be nerfed (both the monster and the race) because every character could disengage, or hide as action and still attack. Also monsters with light weapons and low damage would logically never use the attack action. For example Kobold - attack for 4 damage or dodge and attack for 2. Quicklings could never be hit or targeted in melee; take disengage as an action and move 120 feet and make your light weapon attack without causing AOOs.
2. At low levels 2 points of damage is significant. For example Goblin Fury of the small is once a day and 1 point of damage at 1st level. This is not an issue at high levels.
3. Dodge action: This would allow attacking and taking the dodge action every single turn. Also running something like Hex, Hunters Mark, Smite and the host of Ranger and Fighter subclass damage bonuses will afford significant damage on this attack while dodging every turn. For example a 4th level swarmkeeper running Hunters Mark could use this to do 9 DPR while also dodging every turn. In terms of metagaming; you arm this character with a short sword, a whip and the sentinel feat and they have a 5' and 10' AOO for full damage while taking dodge and doing 9dpr every turn and the enemy can't escape to target someone else. This is assuming you don't allow a damage boost from the TWF fighting style, if you allow that it is even more OP.
4. Monks and two weapon martials: Monks and two weapon martials are already weak in terms of damage, but they rely on their bonus action for that damage just about every turn. By giving other classes the ability to add damage you are moving them further ahead of Monks and two-weapon guys. Considering #2 above, why would anyone ever play a monk? This is gamebreaking IMO, at least if you want to include Monks in your game.
5 Wizards: Wizards are generally considered the most powerful class and could boost damage just about every turn while casting the most powerful spells in the game. Again this makes the powerful more powerful.
6. Rogue: If you allow SA I think that would be op for a Rogue. Also with an AT you could cast an offensive spell and still land SA which makes the most powerful Rogue even more powerful. The thief would be significantly nerfed as any Rogue could both sneak attack and use an object or use theives tools. This would be gamebreaking as well I think. If you don't allow SA it would nerf cunning action, by essentially giving every class the ability to use these and more while still getting in an attack of sorts.