Even after that big ol' explosion at Lake Valor? That was too elusive for the cops? This almost sounds like real life. lol
Black & White seems to be the only game where the adults present actually had involvement in the affairs of the evil team. It may have been mostly gym leaders, but somebody got involved. I just wish this occurred more often. It's just so perplexing that there isn't any of the such going on.
Sword and Shield too. The adults, like Leon, Rose, Raihan, Oleana, Milo, Sonia, and such handle the energy crisis on their own and spend much of the game preventing you, the child player character, from participating in it. It's only at the climax, when all other options have been tried and failed (culminating in Leon taking on Eternatus itself), that the player character and Hop step up. You are a last resort for Galar because this was deemed a matter for adults to handle until every adult with authority had run out of ideas.
And, of course, people didn't like how the player character doesn't get to take part in things and that the adults mostly handle things offscreen. But thinking about it, this is a more realistic way things would be handled.
As for the explosion at Lake Valor, that would be an act of terrorism, and it's usually a federal agency (like the FBI) or the military that handles terrorist groups, not the local police. Even then, they won't necessarily be able to get there immediately, considering by the time you get there, Team Galactic has already wrapped up and you're just battling the agents who stuck around. It IS an odd thing for Professor Roawn to immediately turn to a trio of kids to go take on Team Galactic though, especially as Barry winds up not up to the task.
Again, the villainous teams are either organized crime groups (Team Rocket, Team Skull, Team Yell, Macro Cosmos--whule Skull and Yell aren't the most organized, I'm speaking of the phrase in a criminological sense) or terrorist organizations (Team Magma/Aqua, Team Galactic, Team Flare, Aether Foundation). In real life, these leaders are either so well protected or so powerful that the authorities can't catch them, or they are local pillars of the community and have gained enough respect that they cannot be caught without bad publicity on the authorities or without crashing the local culture.
The leader/figurehead of said organization is usually a textbook example of "
Villain With Good Publicity," [Warning: TV Tropes Link] especially in the newer generations. Lysander, Lusamine, and Rose were all respectable, successful people working behind a legitimate front.
This gets amped up to 11 in the anime where even Cyrus was presented as a legitimate, sucessful businessman before his role in Team Galactic was revealed.
Even in the older generations, Giovanni was and still is depicted as a crime boss with a lot of power, both figuratively and socially. He always remains one step ahead of the law (and in the anime and manga, occasionally the law is on his side), and he is such a talented Pokémon trainer that they can't stop him even if they could reach him. Only the heroes are able to catch up to him and able to outdo him as a trainer. As for the others:
Archie and Maxie seem to work largely in remote areas where they're unlikely to be caught. They never show themselves to the public as far as I can recall; only the grunts do.
Cyrus does what Archie and Maxie do but take it up further and rarely shows himself even to the player character. Even then, he only does so because he thinks he can sway you to his way of thinking, and he never stays in one place for too long except at Spear Pillar. He is not even present at the Team Galactic base in Eterna City. The Team Galactic Grunts, meanwhile, adopt Cyrus's strategy of constant movements. You may battle them here and there, as well as the commanders, but they stick around only for a short time. The only part of their plan you actually foil until Spear Pillar is the one at Valley Windworks, which was a relatively minor thing. For the other cases, by the time you've reached there, their plans are either at near completion or has already completed, and they bail out. Even when you rescue Azelf, Uxie, and Mesprit, Team Galactic had already taken what they wanted from them and they are of no further use to Team Galactic.
N shows himself to the public a lot, but the citizens largely consider him as an eccentric cult leader. No one sees Team Plasma as dangerous until near the end. Ghetsis, meanwhile, doesn't make public appearances at all and doesn't even bother to meet the player character until the end.