This is the standard answer everyone gives, and it makes no logical sense. I worked search and rescue, and have plenty of friends that have it as their full-time occupation.
Search and rescue personal are trained professionals, who willingly signed up for that career, and who love being in the back-country. They know full and well what they're getting into, and going out and rescuing people is the definition of their chosen career. If there was nobody to rescue, they wouldn't be able to support themselves doing what they love.
In fact when there are no rescues for a while they go out in their helicopters and practice all the "dangerous" stuff putting their "lives in danger". So even if there was nobody to rescue, they'd still be out there.
Following on from your logic, it only makes sense we should ban open fireplaces and cigarettes in houses because that's the leading cause of house fires, which then put fireman's lives in danger.
> and costing the public hundreds of thousands of dollars
Please don't exaggerate, it detracts from the discussion.
The average heli rescue costs around $10k (heli's are smack on $1k/hr), and in many jurisdictions if the person getting rescued was doing something stupid, they foot the bill, not the public.