It does not take any sort of deep analysis to see that action stories set in modern times are popular, whether we’re talking about film, TV, or books. Superheroes fighting evil overlords, rebels toppling oppressive empires, and ordinary folks unloading hot lead into zombies and werewolves capture the imagination and speak to the reader in the primal language of survival or death, freedom or submission, truth or lies.
However, we do not live in primal times.
We in the developed West (as well as Northeast Asia) live in a thoroughly modern world. Nowhere is beyond the reach of officialdom’s enforcers; not for nothing do Americans speak of the “long arm of the law.” Flying around as superheroes do will get you punished by regulatory agencies like the Federal Aviation Administration or the Department of Homeland Security. Reliable policing means that private violence of all kinds — no matter the motive — will put you in handcuffs, and “I was fighting bad guys” is not a defense. And it’s not just the government that would crack down on you; everybody has a camera and a Twitter account, so your “heroic action” can be spun as something else entirely. Even calling out a threat to the public can cost you your job.
How, then, does a heroic action story set in modern times resolve this? There are seven ways:
(1) The heroes are part of the official security forces — usually police officers, government spies, or soldiers, and the boundaries between these can be fuzzy depending on the setting or the mood. While it allows the heroes to take violent action against threats freely, they are still limited by government regulations and by politics; however, such limitations are essential for drama (Examples: 24, James Bond, etc. The anime series Naruto and Yu Yu Hakusho are interesting variations on this.)
(2) The threat is too powerful for the official security forces to defeat, requiring the services of extraordinary heroes. TV Tropes calls this “Police Are Useless”, and it is ideal for stories about superheroes, such as those published by Marvel and DC. Anime such as Dragonball Z (and its direct sequel Dragonball Super) and Digimon Adventure 02 (especially its later episodes) also fall into this category. This solution, however, is clearest with non-Marvel/DC Western cartoons about superheroes, since many of those center around “kid power” and make adults in general ineffective.
(3) Modern protagonists are whisked away to a world where the law is unreliable. The anime Inuyasha is the main example I’m familiar with, but classic novels such as Poul Anderson’s Three Hearts and Three Lions (reviewed here) and Edgar Rice Burroughs’ At the Earth’s Core (reviewed here) have done the same thing.
(4) Modern civilization has collapsed, forcing the protagonists to rely on their survival skills. This is the basic premise of most post-apocalyptic fiction, with The Walking Dead being the one most familiar to regular people.
(5) The threats are fought in secret, away from the prying eyes of “normal” officialdom, though the secret world may have its own laws. Kid-focused book series such as Animorphs and Harry Potter take this approach.
(6) Modern society is at war, so one is free to brutalize the enemy. The Marvel movie Captain America: The First Avenger is perhaps the most familiar example of fictional heroics during wartime.
(7) The protagonists are outlaws who work outside the official system or rebels who actively fight to overthrow it. Star Wars is the prime example of the rebellious hero approach, while Ant-Man is a good example of a heroic outlaw. The anime Rurouni Kenshin is a softer version of this theme, since the main character carries a sword in a time and a place where it is illegal to do so.
Solution (1) involves being part of officialdom, while (2), (3), (4), and (6) remove officialdom as a constraint on a hero’s actions. By contrast, (5) involves escaping officialdom’s notice, while (7) involves clear defiance of the system’s dictates.
Note that a show’s position can change; for example, Agents of SHIELD begins firmly as a type (1) series, but craters straight into type (7) within its first season.
I believe this is one reason why a lot of pulps from the past are set in distant, lawless places — personal honor and spoken vows, not complex laws and written contracts, govern what is right and wrong; this makes it easier for the reader to suspend disbelief when the hero gets away with violence. Remember that in ancient times, the official law wasn’t always there to protect people; even as late as the 19th century, you had the “wild west” in the US, where local sheriffs mattered more than Washington politicians.
The spread of modern civilization throughout the world — Western or not — has made the average person’s life much safer and more productive, but that is because it clamps down on private violence; thus, pulp-style action looks unbelievable in a modern setting. Things like the seven solutions mentioned above become necessary when you want heroic action in our wonderland of guns, planes, and computers.
No wonder Conan remains popular.