Elites Are More Glamorous/Analysis
As the main page says, the so-called "elite" units from various armies (most prominently and often, the United States Military) tend to be lumped together in fiction with overlapping roles. This can be a bit confusing to people who aren't interested in the nitty-gritty of what goes on in armed forces so, to help get a sense of what we're talking about when we say this, let's take a look in the context of the US Army Rangers. They're a popular choice when a writer needs their protagonist to sound impressive. But first, a barebones history lesson.
The inspiration for the Rangers was drawn from America's colonial experience (sort of) and World War II where the first Ranger Battalion was formed to take part in joint operations with the British, behind enemy lines and with little or no support - material or otherwise. The reason why they were so admired and the original Ranger Battalion was based on them was because they got results in difficult missions that normal troops wouldn't be able to handle. This is because they were created specifically to do that job and when you think about it, if they were put in any other job with the equipment they were given they would be absolutely terrible. When they are in their element they are terrifying.
In addition to that, the modern day Rangers are very much influenced by the lessons learned in Vietnam, which now form the basis for the infamously brutal training course that they undergo. The problem with this is that it prepares the Rangers to fight in Vietnam or, more humorously, a dogless, warm, thickly-vegetated, sparsely-populated, remote environment. That article is very critical of the hype that surrounds the Rangers, but it an interesting read for what happens when this trope is in effect in Real Life. There's another high-profile example that was plastered all over the newspapers at the time: Operation Gothic Serpent.
So the point is not that elite military forces shouldn't be used in fiction or that they're not badass. They should and they are. Thanks to their specialised training they should (in theory) be more disciplined and motivated than the average trooper (who should be disciplined and motivated anyway), but if you want bonus points for accuracy and a true chance to let your special forces shine, you'll put them in a scenario they were trained for, which often involves some research into the unit's history. Why especially did they pick Seal Team 6 to do the honors on Osama Bin Laden? Because Team 6 is the Navy counterterrorism unit. They were the only ones who could move quickly into a country that probably wouldn't let them in, without being seen by anyone or tipping off the target, breaching the compound, capturing/killing the target, and then making off with the body. It was a very specific scenario that they just happened to be perfect for.
Incidentally, some special forces don't even have fighting as their main function. The US Air Force special forces, Pararescue and Forward Air Control, are supposed to rescue pilots who have been shot down and establish air fields in enemy territory/direct important precision air strikes, respectively.
- Anyone can apply to Ranger School, even people in the other branches of the Armed Forces. Passing Ranger School makes you Ranger-qualified, but you don't have to be Ranger-qualified to be in the Rangers, unless you want to command. Weird, huh?