Characters need easily distinguishable personalities these days, so another person similar to the main character is out. Gotou is "colder" than Eiji, like most secondary Riders, but that doesn't mean he's antagonist or arrogant just yet. Even if he doesn't turn out to be the secondary Rider, somehow, the secondary likely will be colder than Eiji too. It's just a way to easily distinguish the main Rider from the secondary one.
The secondary Rider would just need too much screentime to establish himself if he isn't clearly different from the primary one. Even if he's clearly different, something like being even more of an underdog somehow would just make him need too much screentime to establish him adequately. In a series like Double, and probably OOO too, it's pretty clear that the secondary isn't very important, so he won't have that much focus. Making him clearly different from the primary one is just more efficient.