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Look at the number of people that ride bikes downhill vs the number that have died from a flatted clincher or rolled tubular. I've not seen the numbers but I suspect far more have died from just plain old crashing. Lets not even get into being hit by a car.
Going downhill on a bike within your comfort zone of ability is safe you probable do more dangerous things without even thinking about it.
However if it bothers you or is a legitimate concern don't do it. You ride a bike for fun and fitness unless your are paid to do it why do something that makes you uncomfortable? I like to go downhill fairly fast on my mtn bike, many folks my age think it's too fast, some think it's too slow. I enjoy it and it's a risk that to me is acceptable. I get close to the limit of my ability but try and not go beyond. I make sure my stuff works and is in good shape.
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