Those are tough calls for the people in charge of search and rescue operations. Unfortunately, the responsibility for those things often falls to local sheriffs, who have limited budgets, limited staff, and who are not experts in the highly specialized field. Many of the people who do the hard work in miserable weather are volunteers, and their safety is as important as anything else.
The way the laws are written in the US, responsibility for S&R usually defaults to county sheriffs. In Colorado where I live, that's often someone who has a vast area to patrol with a handful of people. That means important business can go unattended even on a good day. Coordinating an effective search can be a huge job, especially in the sort of terrain where people tend to go missing out here. Help is available, but the practical reality of it is often a patchwork of bureaus and agencies doing their best to work efficiently in difficult circumstances. There has been talk of making the job a state responsibility by default, something that makes a hell of a lot of sense in a place like this. There are many state level efforts at promoting the tourist industry here. There does not seem to be a shortage of money or resources for that.
Having a small staff of specialists trained in S&R, ready to go out and coordinate such efforts would be a huge help. They would be working at building and maintaining relationships with local authorities when not actively carrying out searches, which would be most of the time. You'd have outreach, education, recruitment of volunteers at the local level, people with knowledge of who to call for what and where, with contact information in their phones. Such things exist at the state level in all sorts of other areas where many different people and agencies need to work together. Wildfire management is one obvious example. Search and rescue is just an area that has been neglected.
An example of the sort of problems that should not exist is the fire department and ambulance situation in a nearby town. There is the incorporated town, and a huge subdivision next to it. Each has a fire department and ambulance crew. As one might guess, many of the firefighters and EMTs are members of two or more such agencies. That means they have to deal with many bureaucracies, from town government to the sheriff's deparmtent and so on. Each agency has its own paper work, payment system, and equipment requirements. All of those volunteers have to spend time dealing with all of that stuff instead of going out for practice, or just having some time off. There was an effort some years ago to combine all of that in one emergency services district or some such entity. There were two ballot measures established, one to create the district and one to fund it with a tax mill levy. As often happens here in Murricah, the creation of the district passed easily, but the funding was voted down. Officials were then put in a very awkward, no-win situation where they were legally required to set up the entity but didn't get a penny with which to do it. To their credit, they managed to cobble together a workable solution, but it was pretty much the opposite of an improvement in efficiency.