I guess that depends on how you think about risk - if it's about some probability of an unfortunate event, or maximum unavoidable damage in case of that event. A 1/10000 chance of certain death doesn't sound like something I'd like to take.
(maybe I was a little bit off, it's more likely that the risk of failure is 1/1000, so sum is 1/1.000.000)
but the point is, it's more risky to drive back home after the weekend than to recreational cave dive, especially with dive fatigue!
I think that's the same issue with risk assessment and mixing up probability and impact: A problem when driving home is not a 100% certain death sentence, and it is not something you could not mitigate. You can drive slower, try to avoid dangerous streets etc. And even in the event of an accident you have systems that might save you (airbag etc).
In particular, with something like cave diving and mountain climbing the "bad" outcome is going to be death of the individual or their friends and it will likely be the result of a series of bad decisions under stress (each of which makes the situation more dire) rather than an exceedingly rare multiple systems failure.
More than one death per 100 million miles gives worse than 1:10 000 odds per 10 000 miles. If you do not want to take 1/10 000 death risks, you would need to limit your lifetime car travels to way less than 10 000 miles.
Having said that, I don't own or drive a car ;)
And particularly, don't share roads with any drivers doing any of the above.
And, given so small probabilities, even if you tell yourself that you are mitigating the risk by not drinking&driving, it is virtually impossible for you to know that you do not have some other habit that increases your death probability to the average levels or above. Are your reaction times slower (or faster) than other peoples? Do you hitch a hike always in a car that is properly taken care of? Etc.
And if you do not own a car, your lifetime cycling quota in the US cycling environment is less than 2 000 miles[0]. Even less mitigating other peoples' mistakes than in a car.
[0] http://www.mrmoneymustache.com/2013/06/13/bicycling-the-safe...
Without knowing anything about car accidents, I would say you're very off on that assumption.
Everytime there's an accident involving more than one car, it's unlikely that all drivers involved were at fault.
I think the real difference is not necessarily how safe or dangerous one or the other is, but one is a risk that is practically necessary to function in society while the other is not.
A lot of the risks are mitigated by proper gear and training, just like driving.
Don't dive too deep on air to avoid nitrogen narcosis (similar to don't drink and drive).
Dive with a buddy.
Dive with team and individual redundancy.
Do not silt out the cave (the way you kick and your proficiency in the water has a lot to do with this).
Always have a continuous guideline to the surface.
Reserve at least 1/3 of your gas for emergencies.
And in practice there's other rules -- like you should always sight-see or use cameras/videos on the way into the cave. On the exit you should be more efficient (effectively this usually means you use 1/3rd of your gas to enter, and only 1/4 of your gas to exit, which means you have a higher buffer should anything go wrong).
The redundancy figures quoted are also low. I've done around 200 cave dives. I've had one hose blow on me in a cave and therefore lost a regulator. I can't think of any other local divers who have had a similar situation where they've actually needed to exit a cave with a failed regulator. I would say the failure rate is most likely closer to 1 in 1000. But even taking 1 in 200 as the failure rate, the chances of three failures are 1 in 8,000,000 and even then you can buddy breathe off of a single remaining regulator and you should still have gas supply to exit (the remaining third is there for that kind of situation).
And now I'm more careful to not only get my regulator serviced but to be more aware of changing out hoses and to do so before cave trips if there's signs of wear.
Generally with cave fatalities there are blatant issues, such as failure to maintain a continuous guideline leading to navigation errors leading to simply running out of gas because nobody was paying any attention.
There's only one known cave diving fatality where all the rules were followed and diver still died, which was the cave diving fatality that killed Parker Turner.
Your chance of certain death is 1.
It's only a question of when.