I've been involved in two helicopter rescues in the remote mountains. One was pre-cell phone, and that one took 9 hours from when I first stumbled on the injured party until he was flown out. The first helicopter couldn't lower down to him, so they sent for an army helicopter with well-trained people. He was unconscious for about a week, so injured pretty badly.
The other was my first use of a cell phone. I didn't even know which buttons to push, but somehow got through to 911 and our injured party member (broken leg) was rescued a few hours later. He's still climbing mountains like crazy.
So yes, it takes time, and knowing first aid can be vital. Our county which is rich in trails and mountains and a large population has a very active search and rescue group with a dedicated helicopter. But many others don't have a well trained team and equipment.
Last November I pushed our InReach SOS button after we found a deceased person (the ski3pins were on that trip). That process worked very well -- they really took care of us. The authorities showed up within about 2 hours via ground. It really helps to pair a cell phone to your InReach device as there was quite a bit of back and forth "texting".