>>36145993There's the burglar, the punk and the biker classes. Crime does exist in the Pokémon world. Team Rocket are a literal Mafia, inspired by the Yakuza. The other Teams are more super villain-like up to Gen VI, when Team Skull are vandals and robbers.
As for poverty, it ought to exist. There are the Elite, Socialite, Ace classes, as well as the rich guys in Sinnoh; and luxury stores and hotels in Sinnoh, Kalos and Alola. There's also construction workers, fishermen, office workers, clerks, cameramen, etc. Those obviously have less money. Hell, there are items that cost more than what the player can carry (Master Ball and Bike in gen I.)
The games are seen from the perspective of a middle-class 10-year old, so he probably doesn't understand or care about that sort of stuff.
While being a trainer seems to be a lucrative career, since the player character can always pay for their living expenses, it should be noted that in the Pokemon world it is rare to be a good Pokemon trainer, judging by how most trainers are very mediocre and have weak Pokemon