No, the animated series took directly from the movie characterization. Goyer and others had already devised the character. The animated series used it first. The movie version was developed first, and they used that. Same with the anime. That's like saying Batman or Vampire Hunter D or Samurai Jack don't work as characters. Same basic skeletons.
It's a weird opinion to say the most popular and nuanced version of Blade is boring when that's literally the only version of Blade we've seen for close to 30 years. It took what worked from the original concept and improved upon that character while preserving his most integral character traits and origins. Ultimately, making him more unique and a better fit for the Marvel Universe.
One of the things that makes Blade so popular is that he has a very basic internal struggle. Blade is a dhampir hunting vampires. He's dedicated himself to hunting a part of him. He has an inherently conflicted nature. Hating a part of himself. Can he overcome it? Be better than it? This disease that was forced upon you. This disease killed his mother. His job is to go up against the very thing that he could be. He's continually fighting the man in the mirror. If he can be better and persevere he triumphs for himself as well. Blade's mother was taken from him by vampirism. The foster woman who raised him met their ends to vampirism. The loves of his life. His trusted friends and comrades who he's battle alongside. Blade, to a degree, is a pariah in his own vampire hunting community and not fully accepted or embraced because of who he is. He has a very tragic and compelling story. There are constant betrayals. He has to track his enemies and determine who he can trust and not. He moves within secret channels, with few allies earning income and supplies where he can. Yet, despite all this, the essence of Blade's struggle is very relatable. Overcoming the odds in a society, a world stacked against him, losing his parental figures and guardians at an early age
Here are two videos that exemplify the essence of Blade
https://www.youtube.com/watch?v=ltYFYvoQpkg
https://www.youtube.com/watch?v=bVJmHgDxo6A
The live-action tv series wasn't truly a Blade series. He was a secondary character because they didn't get an actor to play him or write him as a character. Any competent writer can craft a compelling story around Blade the way he is now. I know this because I've seen it done countless times with similar characters. Highlander, Vampire Hunter D, Solomon Kane, the Witcher.
It sounds like you aren't a big fan of any of the modern Blade stories in the last 25 years comics, animation, or live-action. I'd recommend rewatching the first movie, not the others. It's actually far more nuanced than you are making it out to be. Every positive Blade work (I've listed them before) is merely an update on the character. As the new movie will hopefully be. You can't poo poo what came before. Without the first film, we might not be reading about Blade's character anymore. I remember pre the Wesley Snipes film when Blade was described as the jive-talking Black Van Helsing. I'd push back on that too. Wolfman's Blade served to inform the film, just as the film serves to inform the current stories. They are all tied together. You don't just go from 0 to 100. There is a build-up, a continuity of history that Blade embodies.
Therefore, to go down this rabbit hole of Blade is boring or lame over a bad comic seems completely out of context to me.