At my table, it is generally understood that Dragonborn are mechanically underpowered but flavourwise really cool. For the purpose of this question, I'd like to just take these opinions for granted. In an effort to bring them to par with other races, I've started putting together a variant dragonborn homebrew. One of my players suggested a natural claw attack which would be functionally identical to the Tabaxi's, e.g. 1d4+STR Slashing damage natural weapons. This seemed at first glance to be an easy include for me, because it works to our idea of Dragonborn flavour and doesn't seem particularly powerful, since most Tabaxi I've ever seen never even use their own claw attack in favour of actual weapons or spells. This is even when DMs house rule Tabaxi claws as Finesse weapons.
Are natural attacks particularly useful outside of rare circumstance? Can they be optimised in ways weapons cannot? In short: do they realistically affect race balance?
I understand that natural weapons are useful when you've been captured, disarmed, or otherwise caught unawares, but I struggle to imagine a way to make them more than just a rare convenience.
Note that this would not be the only change I make to Dragonborn to help my players enjoy them more, but is on the table as one of many potential changes
Best Answer
Generally speaking when looking at racial balance, a good starting point is the Detect Balance sheet.
It's designed for people making their own races, to get a feel for how strong something is (or isn't). It shows that Dragonborn are on the weak side, too.
The sheet lists a 1d4 natural weapon to be worth 1 point, which it describes as "A ribbon, not likely to make much difference". This is, as you mention, unlikely to be very useful. The score goes up a little when you make stronger natural weapons, or make them not use a free hand.
Indeed, these natural weapons rarely come up. Anyone wanting to deal damage with weapon attacks will have better options (unless you do something outrageous, like a 1d10 natural weapon) and anyone not wanting to make weapon attacks will rarely make use of the slight improvement over a regular punch.
You might see the occasional attack of opportunity made by a Wizard, or the natural weapons used when the party is somehow not able to draw real weapons or has their hands full (literally). And that's about it.