The "crossover" genre is, for the most part, a distinctly Japanese genre. While there are examples of crossover games with a western genesis, the majority of them - from Super Smash Bros. to Kingdom Hearts - are produced by Japanese game developers (Nintendo and Square Enix, respectively).
While it's easy to create a crossover solely to diversify a character roster (e.g., fighting games), it's an entirely different manner to create a crossover with a coherent narrative. This is where Japan exceeds the West. Many of the crossovers gamers love, from Professor Layton vs Phoenix Wright: Ace Attorney to the aforementioned Kingdom Hearts franchise, are juggernauts that overshadow a virtually nonexistent western industry.
Perhaps the first example of the Japanese crossover industry is exemplified by the game Battle Soccer: Field no Hasha. Released exclusively in Japan in 1992 for the SNES, Battle Soccer is unique not only in the sense that it's a crossover game but also in its notoriety for transcending gaming franchises to encapsulate characters from various Japanese media franchises such as Godzilla, Kamen Rider, and Gundam.
The Japanese crossover has since evolved, taking life in various forms across all gaming genres. Since the days of fighting games, the Japanese crossover has become a versatile staple of the gaming realm. Because of this, we get to enjoy some insane crossovers, some that most people wouldn't have ever anticipated. I bet three years ago no one could've foreseen the fruition of collaborations such as a Pokemon and a Nobunaga's Ambition crossover. Even the most rigid gamers can't gloss over the legacies Super Smash Bros. and Final Fantasy have left so far.
Crossovers are unique in the sense that they provide new opportunities for gamers. They can enthrall the imagination and open gamers' minds to new worlds of possibility - especially when we add a narrative into the mix. Yeah, no one probably anticipated a scripted interaction between Mickey Mouse and an ARPG protagonist, but it's refreshing nonetheless, prompting players to wonder just how the iconic mouse would fit into the Kingdom Hearts universe and his relationship to said universe. The same could be said about Professor Layton vs Ace Attorney. This is a notion that alludes many western titles, and even some Japanese ones, like the aforementioned fighting games that don't delve into the lore and narrative of their respective worlds. The only western game that comes to mind that follows a similar trajectory is Nicktoons Unite! and its sequels.
Still, it's easy to understand why people aren't necessarily fans of crossover games. Some are just so baffling and completely came from the left-field that people aren't sure to do with their existence. "Why? Was this even necessary?" may be a common response to these sort of crossovers. And it's true, some crossovers are just so completely bonkers that it can make some question whether the game is of actual quality or simply a way for developers to promote their franchises and snag some extra dough. Regardless of how some may feel about crossover games, they are a legitimate source of entertainment - whether you're duking it out with your favorite Nintendo characters or exploring various Disney universes with Sora, the Japanese crossover is an integral part of our consciousness.