There is definitely overlap between anime and traditional cartoons, but the two mostly cater to different audiences. This doesn't stop Western animation from paying homage to anime though, as the style greatly influences cartoons even to this day. One Western show's entire premise was homage to anime, though it flew under the radar. This is the Nicktoons Network original series, Kappa Mikey.
Nickelodeon rarely uses this anime-esque style even now, so it's interesting to look back on when it did. Kappa Mikey premiered one year after Avatar: The Last Airbender, which is arguably Nickelodeon's biggest cartoon of this variety, so much so that people consider it an actual anime. However, the series had poor ratings and didn't last that long, though it had plenty of potential.
The show revolved around Mikey Simon, an American who won a contest, traveled to Japan and got a job on a has-been anime, "LilyMu." Kappa Mikey paid homage to anime in every episode with its over the top humor and facial expressions, as well as its art style and its many references to popular anime like Speed Racer and Yu-Gi-Oh! Cartoon Network was airing anime-influenced cartoons around this time as well, such as Teen Titans and Hi Hi Puffy AmiYumi, but also aired genuine anime at night during its Toonami block, embracing the medium more than Nickelodeon. In fact, Kappa Mikey didn't even air on regular Nickelodeon, it aired on the secondary channel: Nicktoons Network.
Nicktoons Network wasn't available on basic cable packages like Nickelodeon was, so it didn't reach as many homes. That certainly didn't help the show's ratings. Another downside was that the show didn't have the best production value. It was put together with flash animation, which made character movements look stilted and choppy - not quite up to today's standards. There was also an abundance of fart humor in the show, rather low-brow comedy that didn't age well at all. Regardless of those issues, Kappa Mikey was a unique show and ahead of its time, embracing anime and anime culture long before they became as widespread as they are today.
While there was an anime market in the West during the 2000s, it was still considered niche material. It wasn't appreciated at the same level that cartoons were at that time, but it was certainly growing. That's why shows like Kappa Mikey were created, to try and capitalize on that market and the crossover appeal. However, compared to the stunning visuals and incredible storytelling of its contemporaries like Avatar: The Last Airbender, it fell by the wayside. Once Kappa Mikey was off the air, it was largely forgotten. The network never mentioned it again and it just vanished from the public eye.
If Kappa Mikey were made today, it would likely have far more success. The anime market is much larger in the West now than it was around the time of its original broadcast. Anime is referenced and directly influences more cartoons than ever, from She-Ra to Steven Universe, as well as plenty of other media. Not to mention, there are more live-action adaptations of anime series than ever before - premiering in American theaters, no less. Anime has reached a level that it hadn't yet in the mid-2000s. Kappa Mikey's biggest mistake was that it jumped the gun. Hindsight is 20/20, but had the series released just a few years later, it would have caught the third Western anime boom and benefited from actually reaching the audience that'd appreciate it the most. Kappa Mikey is an often forgotten series, but it was something different that people didn't see a lot of at the time or even today. Maybe one day, the world will be re-introduced to Mikey Simon and the rest of the LilyMu cast.