Given that scenario as stated? Sure, I'm all for it. Take away the gloves in boxing and we're pretty close to that.
I'd be concerned about the negative incentives that could potentially exploit lower income people, but on its own I don't have a problem with it.
I personally wouldn't do it, and I don't think I'd enjoy watching it, but I'm of the opinion that:
1. If it occurs a lot, there is a market for it,
2. Given a market for it, we should explore allowing and heavily regulating it, including negative externalities, rather than banning it and pushing it to a black market.
https://en.wikipedia.org/wiki/List_of_deaths_due_to_injuries...
So, while companies should have workers' comp and provide helmets on the job, it doesn't mean that the risk needs to be zero. Dangerous jobs tend to be well-compensated, so it either comes down to risk tolerance or cultural factors (something like "my father was a miner and I live in coal country") more than desperation.
Could you cite some evidence that this is a widespread attitude? My knowledge of miners, which is very little, says something much different.
> Dangerous jobs tend to be well-compensated
I'm not sure that's true. In the list of high-paying jobs that money-motivated people aspire to, I usually don't see coal miner (or any miner), soldier, police officer in dangerous neighborhood, logger, deep sea fisherman or drug dealer listed.
If we are talking where death is a risk but not a definite, then we do allow such jobs. At what point do you consider the harm too bad to allow and would we really consistently apply that standard?