Park ranger and search-and-rescue/first responder here.
1) National Parks are fucking HUGE. You often have no idea where in the park someone was before they disappeared, much less where they wandered off to in the hours or days since someone last saw them.
2) Parks are chronically understaffed, and the majority of personnel are interpretive rangers, not law enforcement. Interpretive rangers are basically glorified tour guides and janitors, and most have only the most basic training in search-and-rescue.
3) When someone goes missing in the woods, there often isn't much of them left to find if they die. Mountain lions, coyotes, buzzards, pigs, bears, badgers, etc. all eat dead bodies. The natural bacteria, fungus, etc. decomposes bodies faster than in, say, an abandoned building or some serial killer's basement. Typically, if someone dies in the woods, all that's left to find is skeletal remains, and you try finding some bones scattered by scavengers, buried by leaf litter, and lost somewhere in the woods in an area that's hard to access and is the size of a major city.
4) Search-and-rescue dogs are not infallible. My dog is typical of most dogs and is easily distracted; I have to keep her focused on the task of looking for a person, not chasing squirrels or eating a dead rabbit she found under a bush. She gets tired after a couple hours. She doesn't like going through dense brush, thorns, etc. any more than you do. Being able to track someone's scent is dependent on how recently they passed through, how much spoor they left behind (sweat, blood, etc. on soil is better than just the soles of their shoes stepping on solid rock), wind speed and direction, how dense the trees/brush are (the denser, the less scent), etc. The majority of scent dogs cannot track a specific person's scent and simply home in on the nearest person, which may or may not be the one you're looking for.