Just got my first gravel bike so apologies for the newbie question…
I might decide to go for a road bike shaped bar (this bike will be used for a mixture of road and trail). Do people typically err on the side of overbuilt bars (not too light, maybe even aluminium) for strength, or just assume that all road bars have more than enough margin of error to be safe?
I think all bars are safe enough. Question is do you want a flair on the bar. A lot of gravel downhills you might want a flair since it won’t feel safe in the hoods
I think this is an ‘it depends’ answer. If you’re a fairly light rider, and don’t intend on doing anything more than light gravel, carbon road bars should be fine. If you’re heavier, or plan on ‘harder’ off road riding, I’d be cautious.
I could go off on my regular rant that weight on a bike is much less important than everyone seems to think it is, but I’ll spare everyone 
If in doubt, I would always err on the side of strength/durability. The extra 100g will make no measurable difference to your speed, I promise you, and the difference in ride quality will be very secondary to tyre size and pressure.
The biggest benefit of Carbon bars on gravel is the comfort. I don’t care so much about the weight, but they do a much better job of killing off some vibrations that aluminum doesn’t.
I run Salsa Carbon Cowbells, they are a very light(12*iirc) flare bar.
Thanks guys. My bike has come with cheap and heavy flared bars - I’ll run those for a while to evaluate the shape, and then decide what to fit permanently. Part of the reason for my question is that I have a couple of light road bars sitting around already. I totally agree that losing bike weight is generally overrated, but if I’m going to swap something out then clearly I’ll swap it for something better, even if the weight difference is imperceptible! 
I run enve road bars on my gravel bike and raced it as well. I was 180 ish at the time and had no issues on some really bumpy fast sections of SBTGRVL. Never ran flared bars but I hate the way they look.
I also run the Salsa Carbon Cowbells on my gravel bike and they are solid and highly recommend them.
I have an old specialized diverge (2017) which is less a gravel bike and more and adventure bike (tire clearance max 35c) that I popped some s-works shallow drop carbon bars onto. No flare whatsoever as I wanted something that was at home on the road mostly but I did gravel with anyway. These bars have been everywhere New England gravel has taken me from road to dirt to single track. Had noticeably less hand fatigue and they lightened up the bike quite nicely. I’ve fallen over with them a few times and even crashed and they’re still holding up just fine so yes carbon for gravel is fine. I’m speccing out a gravel frame build and am continuing the carbon bars with some FSA k-wing AGX bars so clearly I’m confident in carbon’s ability to survive and thrive in gravel settings.
I’m in the Salsa bars camp. I dumped the carbon road bars that came on my Giant Revolt for the wider Salsa bars to improve control in the chunky stuff down hill. Yep, sacrificed some aero but I’m big shouldered anyway.
My Cervelo Aspero came with aluminum Easton flared bars but I didn’t like them. I went to a 40cm Thomson Road carbon bar that has a slightly ovalized top section and no flare and I REALLY like them. I use carbon Specialized Aerofly bars on my road bike. Ditto the comment about reducing vibration. This is often misunderstood, carbon bars are typically (not in all cases) stiffer, but the nature of epoxy/fiber means that the little vibrations are smoothed out. I’m a light rider, but I’ve ridden this bike/bars on some really rough trails and not babied them at all and they are solid.
Failure of any carbon component typically occurs in a crash event or after being hit by a sharp and/or hard object that causes a crack, not from stresses during riding.
I run Thomson 44cm road bars on my gravel bike - I love them and have never had an issue.
They also make carbon gravel-specific bars now with flare, but I don’t care for that shape, personally.
Good luck 