I don't know if I would say iconic. I'm not a huge Superman fan regardless, but Doomsday was always more like oh look, this beast that killed Superman. It's like Professor Zoom, quite honestly, he isn't that well received as a Flash villain, yet he still had his schemes against Flash. Source material is also a circumstantial thing. If you honestly went the route of having DD origins like in the comics, he probably would never have a live action iteration. Considering Lex is cheap and easy, all Superman movies would essentially just be Luthor.
I also don't understand why people constantly compare Eisenberg to Lex when, he isn't the Lex Luthor everyone knows. Yes the *******ization didn't help, but he isn't at all the character of Lex Luthor, I found the moment of him mentioning his father and the parade as a good like take of why someone like a Luthor would despise such people.
As for the twitchiness, it also is to throw off the scent. No one at any point figured Luthor had pulled all the strings. And some ask why would he even want to duke out Bats and Supes, but he literally already mentioned Darkseid. I get people want methodical and reasonable, but ironically enough, everyone loves Ledger's Joker. If you honestly plan it, Joker had everything worked up right until the end, but he always introduced it as him having no idea what he is doing, or just going with the flow. Luthor has done the same exact thing, yet he gets flak? I always admire those types of villains, just like why I like Quatum of Solace, cause Greene was not some brute or mastermind, or supreme villain. He was just a guy that got put into a corner against an incredible spy, but he always had Bond at a moment of hesitation. Probably not a good point, but too much methodic planning just goes to **** too like Baron Zemo.