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Gen 3's aesthetic is purely utilitarian, it exists solely to facilitate gameplay. It's the fastest and smoothest the series has ever, and will likely ever be. It's not as cozy or artistic as the gens before or after and lets the gameplay tell a different story. Meaning it is a goal oriented game, instead of "let me go exploring, and see new Pokemon" it's more focused on "items, stats, grind, collect, organize, battle". These things are common to the entire series but Gen 3 uses visuals to make the core gameplay more accessible and puts it at the forefront.
They had a chance to reboot the series and they took it, the fad had died after the release of GS and they threw everything out and started from scratch. They redesigned all the characters, the Pokemon, and created the key art that would be the foundation for the series moving forward. This got rid of a lot of jank but also a lot of the charm and soul people miss about the early series. It was all done to sanitize and create an accessible entry point for new fans and not have to rely on old fans that had bailed on the series after GS. Not only the visuals were rebooted but the entire data structure was overhauled to what would become the core of the series.
Gen 3 will never get the recognition visually that other gens get since it doesn't have the nostalgic appeal since it never goes away. From romhacks, to nuzlock, to difficulty mods, to randomizers, to battle factory, to shiny hunting, it's omnipresent and eternal. The oversaturated Y2K merchandise-ready aesthetic never had a chance to go out of style and be called "SOVL". Gen 3 suffered from its own success and becoming the defacto base for mods and alternate game modes that kept it relevant in the era of youtube and streamers.