I will try to answer this one. (scary :O)
In the anime and the games there have been children with Pokemon and Max and Bonnie can't have one. Well my theory on this is all about parents and laboratory policy. I think the laboratories' professors won't give a child a Pokemon until they are at the supposedly responsible age of ten years. But the parents could obviously give them a Pokemon of their own, right? Well this is where a parent's responsibility comes in. In real life and (I think) the show different parents have different views on how to raise their children. Some say give them the responsibility early so they can build character to be a fine adult. Others want to shelter them a little longer because they can't handle such responsibility. Of course with Max going on the journey with them and all that, it might dispel that theory. MOVING ON
I actually haven't watched all of Pokemon so I have no idea who the Pokemon Bros. are. MOVING ON
I am, however, past the original Kanto series and I don't remember the Pewter City gym nearly being shut down so is it later on? MOVING ON
Kas and Yas makes sense to me, though. The Pokemon league is actually a pretty organized league, and you have to earn official league badges from the gyms to compete blah de blah de blah. For the Pokemon league to be trustworthy they must have good, strong gym leaders, with a fair and open mind. If not, then maybe they would be too angry to give them a badge when defeated. This (I think) is what is going on with Kas and Yas. These ruffians were way too immature to be officially giving away badges.
In conclusion the writers are probably trying to make things as realistic as possible. And in the way often said on this site: The writers for the games and the anime are different people. The games and the anime are not the same thing.
Hope I helped or at least made sense (It's hard to present ideas through writing)