I really, REALLY like Asakura Takeshi. Am I biased because I'm a simp for him? Yeah. Am I still gonna defend him? You know it. A lot of people don't really like Asakura, and I get that. He fits the archetype of the 'psychopath villain' who does evil things just to be evil. This kind of character can be annoying because their actions have no motives, which can feel unsatisfying to the viewer. Personally, I think Asakura has enough unique attributes that set him apart from the average Crazed Villain like the joker.
Asakura doesn't act totally illogically. He has a motive, and even a set of morals - they're just both mostly mad fucked. Asakura's goal is to repeat the rider battle over and over, so he can continue his rampage of murder. Thus, everything he does is towards this motive. Despite this, he holds himself to (admittedly loose) morals. Asakura won't kill someone if they're unarmed. He refuses to kill fellow riders if they haven't transformed, because he lusts for the thrill of the hunt, not simply for their deaths. I think this is a great writing choice because it addresses a common complaint - 'why don't riders just steal other rider's belts?' Aside from the fact that this does in fact happen in the show, the fact that Asakura - who kills the most riders in the show - would refuse to kill a beltless rider is reason enough not to steal someone's belt. You're reducing the likelihood of them actually dying, and much increasing the likelihood Asakura will come for you.
He also doesn't kill kids... Sometimes. Low bar, I know. But there are times where he has every reason to kill a child, and doesn't. He's not totally, 100% deranged. Just mostly! But it's these little things that take a character that could have been just another 'crazy psycho' and give him defining characteristics. There's a lot to Asakura - he's Shiro's favourite, and knows it. He's deeply intelligent and sly, yet uses that cunning for horrific, savage motivations. Shinji struggles to reconcile this, and it's a moral problem he has to grapple with. I just think he's neat.