Not entirely arbitrary for Ken. He's the "original echo fighter", which does make sense why he got that label. That's something people forget that he also said that.
He's still far less different than Dr. Mario, as the differences in their attributes and movesets are quite apart. Dr. Mario is just the least cloniest of the regular clones, but still vastly different from Mario. Ken? He still shares quite a lot with Ryu, including the same actual gameplay mechanic(it's just that they have different move commands like their home games).
Ken is the only Echo Fighter who could've easily not had it, though, true. It is also worth noting that Dr. Mario wasn't always the same weight as Mario, as the final version of Melee gives them different weights. This does explain somewhat that Sakurai doesn't see him as Echo material because he sees that he has too many different attributes throughout the franchise. Ken cannot say this within Smash itself, and probably never will.
Huh, the same article says PP is a he? Strange. You'd expect they'd go with It. Then again, may be an odd translation.
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As for how they've been handled; they're blatantly different forms of Clones. Even Ken. The idea is they barely have different attributes(sometimes none), must share the same bodyshape, have clearly been the same weight(Reggie's observation makes sense to why he thinks that's an actual requirement), and their differences will never equal that of a more regular clone. Ken, as I noted before, is actually quite a bit more similar to Ryu than Dr. Mario is to Mario. This doesn't mean the Echo label actually fits(it's not entirely arbitrary, but it could go either way too).
The problem comes with not giving them something slightly more. Dark Pit comes a bit too close, but Dark Samus has a different element which separates them enough in Spirit Battles at least. Richter and Simon need a slight bit more, as they barely are different thanks to how their Holy Waters interact with items. Chrom and Lucina are good. Ken is a nuff said on being perfect. Daisy is the only one who hard suffers from lack of differences. While Richter is also pretty bad, Daisy only has... a hurtbox difference here and there, but it's so minor it means nothing even in casual gameplay. She doesn't need much either, just some custom moves or returning the Turnip mistake they made earlier.
I don't know enough about Richter, but Simon has more moves he could use anyway to help further separate them. As for Dark Pit, using any item from Uprising could be enough. Sure, more than just a "few differences" is good too(Lucina and Chrom lacking a type of sweetspot vastly changes how they play. Ironically Ken's thing is just a different moveset combo here and there but plays a bit more like Ryu than one would expect for someone so "different").
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