Asklemmy

If I now say that your premise is wrong (headphones don't cause hearing loss, loud noises do, independent of the source), does that automatically answer your question? 😛

Now to dig a bit deeper into that, there is a lot of research into MIHL from using PLDs, and the key thing is always people turning up the volume higher than they normally would, usually due to the context of where they are. That is, we use our little headphones in noisy environments, and to drown out the noise we turn them up too much and start damaging our ears over time.

In that regard, bone conduction headsets are worse. They are intentionally fully open, and don't in the slightest bit try to reduce ambient noise. That is, if anything you'd be tempted to crank them up even higher.

I will however say that the models I've used all came with an interesting "safety" in this regard that stems from the way they work: At a certain and not that loud noise level, they start vibrating physicially off the skin during playback, in turn plateauing the achievable volume. I suspect however that this level is already beyond healthy.

So, in other words:
If you're concerned about hearing loss, keep the volume in sane reaches. If you also need to ignore outside noise while listening, this means getting enclosing and/or noise-cancelling headphones, not open ones like bone conducting. However, if keeping the volume low, say during listening at home, bone conduction is no different from other forms of receiving audio, both still stimulate the hearing canal hairs.