that's a weird take just based on who the characters were canonically and how the worlds evolved. Beasts genius and powerset makes him an easy fit for the Avengers just like the X-men. It's only weird because in the universe the X-men are often written as belonging to a separate world with non-X-men writers rarely acknowledging Mutant affairs or stories like they don't exist. Whereas, if it was a shared Universe mutant would topics of discussion or seen much more in every day Marvel stories. And I'm aware of the current storylines, but that only applies to recent years and I'm talking about decades here. The Avengers became the team above everyone else and it's where all the top dogs end up.
By the very changes DC made to Cyborg in the New 52 he's a different character. Short of Brainiac, DC doesn't have another technopath like him. He touches the world and interacts with everything in such a profound way. He's a very modern hero, that any competent writer could have made an integral part of the Justice League if they so chose. They made him a cyber god, but many chose not to write him as such. So people think he should stay on the Titans where he used to shine once upon a time, but overlook the fact that the Titans aren't what they once were and may never. They say that Hollywood doesn't have any original ideas and you could say the same thing about the comic industry. DC didn't nurture the Titans brand like it should have, for how unbelievably successful it was in the 80s. If it wasn't for the cartoons I don't think executives would treat it as they do today. The majority of Titans characters aren't treated with the same love in respect outside of the Titans book, there are some exceptions but not too many. So at the time, the Justice League makes sense because that team has changed. That is the marquee superhero team. It's not just the big 7 anymore. The Justice League is that team and every other one is below that. DC might want to change that, but as things stand the Titans and JSA are looked at as assisting the Justice League. The JSA is either a secondary team or an older team but not the premiere (unless they put it on another dimension). The Titans are kind of in a weird place it's an organization that guides and fosters younger heroes and has its veteran members that helped found and define the group. However, these days it's seen as a JV Justice League or a secondary team, some may view it almost like a feeder for the Justice League. If the DC Universe progressed with a more natural time flow many of those members would assume the spots of the more senior heroes. As Batman and Green Arrow retired due to age, injury, or death then Dick and Roy would assume those spots. Donna Troy would step up, newer non-legacy heroes like Starfire, Cyborg, Beast Boy, and Raven would grow into more prominent roles in the superhero community. Between battling Hive, Trigon and Deathstroke it's like they weren't ready for anything, but that doesn't happen. DC has a weird timescale. Batman and Superman haven't really aged in 40 years, keeping the second generation in a confusing age bracket while introducing the fifth generation of heroes.
So while it might feel weird to longtime fans if you look at it objectively in the universe those moves make a ton of sense