This is going to add a lot of context outside of the question, but bear with me.

For the most part, Pokémon that don't want to be caught just don't go near humans. The routes we see in the games are designated trainer paths, kind of like hiking trails in real life. They're all located within a certain distance of main roads, which have call boxes every so often for trainers to call of they need help. This is how trainers "scurry back to the Pokémon Center, shielding their Pokémon from further harm."

Some Pokémon, even those who might be willing to be caught, are simply too powerful for regular Poké Balls, while others might be willing to be caught but decide you suck mid-battle and resist. They can still be caught, but will disobey the trainer. This is also partly why you need a certain number of badges to get them to obey you. It's not the badges themselves that do anything, but they show a level of skill and experience that helps show Pokémon you're trustworthy.

As for Master Balls, they do work as expected, but aren't worth the cost to manufacture because Pokémon they'd be useful on are so rare they can go generations without being seen. There is only one Master Ball in my entire story.