Within the US, if you get injured, regular medical insurance will cover your medical costs (if you have medical insurance), plus ambulance/air ambulance etc, subject to your deductibles and other terms and conds. Some medical plans will also cover you around the world (check before you rely on this). When my mother-in-law broke her ankle in Austria a couple of years ago and had to be helicoptered off the mountain, then spent 6 weeks in Feldkirch hospital, everything was covered by her medical insurance (minus deductibles). Most accidents are treated just like sports injuries, and are covered unless specifically excluded (check your medical plan policies).
COSAR and other SAR funds typically collect to cover primarily search and first response costs... and will most likely NOT be covered by your regular medical insurance (although SAR team members, even if volunteers, are covered by their state or municipality's workers comp insurance if THEY are injured as part of a rescue).
If you don't have medical insurance, you REALLY should get some before you go on an expedition. Until healthcare is universal here in the US, you need it if you get in trouble. Rescue insurance would be great, to get you off the mountain, but the REAL cost usually comes from the medical bills, not from the S&R work!