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Some part of its popularity might be attributed to its prominence in Gen III. For fans whose first game was gen III Rayquaza is very much what Mewtwo was in Gen I. Deoxys is reminiscent of Mewtwo too but in terms of how it was distributed was more of a gen III Mew analogue.
In short, everyone's first game shapes their idea of a "true" Pokemon game, and legendaries feed into that.
The rest of it is probably its meta-game viability, the fact that dragons are a popular type, and of course fug memes.