Why does Gorou, upon assuming Zolda's identity, stick to using ranged attacks, despite being a good hand-to-hand fighter? Because he didn't want to give away the deception to Asakura.
Ren/Knight, despite having little or no qualms about fully participating in the Rider War, can't bring himself to kill another Rider, and the one whom he did, Odin, never really died in the sense of the Odin persona remaining alive. It makes more sense when his status as a Batman Expy is remembered.
Asakura's death scene makes a lot more sense when you realize he's obsessed with finishing what he started. Look at how he manipulated Reiko into tracking down and reuniting him with his brother, all for the sake of getting another shot at him. That was years ago, when they were kids, but he never forgot and was probably thinking about it all this time. Now he spent the whole series trying to kill Kitaoka, and failing. The weaselly lawyer always got away. After what happened with his brother, he probably decided he would never let someone he was trying to kill escape. When he again failed to kill him, it finally drove him insane... well, insaner.
If you watched Kamen Rider Agito, you'll know why the evil Agito Burning Form, existing simultaneously with regular Agito in the Ryuki vs Agito short, isn't that farfetched an idea.note The premise of Agito states that certain humans can evolve past humanity and into an Agito, and it's happened to several characters already (Shoichi, Dr Kino, Shoichi's sister in the past, and Ryo/Gills could also count)
It also relates to how Shinji had a mirror copy who was downright evil.
Ren's later horror for when seemingly killed Odin and unwillingness to kill Jun seems to run contrary to how he didn't bat an eye to when Suuichi was killed by Volcancer after Ren broke his deck, but when one thinks about it, Ren didn't deliver the killing blow on him, Volcancer did, so to avoid admitting to himself that he was responsible for Suuichi's death, he simply thought of Volcancer as the real killer.
In future crossovers, Ryuki and the others appear, rider belt and all. At first, given the concept of alternate universes as presented by Kamen Rider Decade, this might be a good explanation of how they have their decks even when the Reset Button Ending states that they no longer have those, but you then think a bit carefully, and you realize that somewhere in an alternate world, the war never ended. It's more bone-chilling when you consider the alternate endings, where a good chunk of them are Bolivian Army Endings, and one of them ended with the war resetting, just that now Shinji has Ren's deck. Though thanks to Ryuki's Hyper Battle Video and Decade's take on Ryuki, where the riders are either heroes of justice or lawyers respectively, it could be possible that the Ryuki Riders came from those universes.