Not sure about the Eda theory though if it were true it'd be amazing.
The King and Bill CIpher theory though, that's a hill I'll die on if I have to lol.
You'll be missing out on a lot of story concerning Olimar and the background of other things if you go to three, but three is a great place to start from a gameplay perspective. It introduces plenty of new game mechanics as well as mostly improving on those from prior games, and does a good job of explaining the basics. Managing and ordering Pikmin has always been fun to do, so you're set on that front. It also has a time limit like the first game, though it's less restricted and relies instead on how much progress you're making. It also lacks a dungeon system present only in Pikmin 2, so no matter which game you start with or what order you play the games in, Pikmin 2 is always gonna be the odd one out on that front. It's still a great game, but all in all I can agree that three is still a perfectly good place to start, from both a gameplay perspective and considering the fact that it's much more easily available than either of it's predecessors.
The first two Pikmin games have aged perfectly well, imo, just...as long as you aren't playing the original Gamecube version of Pikmin 1. The New Play Control version of it on the Wii has some bugs but it's better than the original simply because Pikmin are much easier to control and save from environmental hazards than in the original.