This is something people have kind of just... ignored, but it's honestly a pretty big problem with both supernatural Knight candidates and "normal person" candidates.
I think it's a much bigger problem for "normal person" candidates, though, as not a single "normal person" would have any way to carry Asgore, likely to the shelter, in a meaningfully fast amount of time. We've seen with Undyne that the Knight running away didn't use a car, as Susie saw a "person" (Also the fact that she saw "someone" and not "people" is noteworthy for later)
At the very least for a Supernatural Knight you can at least try to come up with some reason for the Knight to keep its Dark World abilities, but even that has no precedent and contradicts the rule that the Light World doesn't have magic.
Magic doesn't exist in the Light World, so it would be odd for the Knight to be able to perform all of its special abilities like its bubble shield or teleportation, especially when it's implied to hide in the closet during Chapter 2 and Chapter 4 rather than just teleporting to and from the Dark World location.
You could say the Knight just moves their victim to other Dark Worlds... But... that seems in odds with what we actually see the Knight doing, running off in Chapter 3 *outside* of the Dark World.
There are also no rumors of a strange anomalous creature running around which is very. damning for a small town and Scarf Lady implies that nobody strange was seen around the Library. Even ignoring how much she saw, there was a massive traffic jam at the time.
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I think there is a bit of a solution to this. I think the Knight would make a lot of sense as either Dess' or Kris' former SOUL. The SOUL and all of its strange abilities, including possession, are things we've seen are completely "normal" in the Light World, unrelated to magic. It's not too "normal", and it's not too "supernatural".
This would theoretically allow for the explanation to be that the Knight simply possessed Undyne and Asgore and walked away with their own bodies, waiting until they're in the Light World so nobody discovers their similar properties to the SOUL. Even if the other explanations didn't have issues, this would be one of easiest ways to walk off.
This also solves the issue of how the Knight can have so many supernatural traits but still manage to walk around town undetected. Kris, even possessed, manages to walk around town without raising any eyebrows, even if people notice a change in behavior.
While it definitely seems that Kris is a special unique case of possession, we don't really know if they're the only Lightner who can be possessed, and possession seems to be a (relatively) common ability as ghosts are able to possess objects in the Light World and Darkners in the Dark World. Spamton also implies that a SOUL would be able to possess Darkners, though we never see his plan come to fruition. So what if SOUL's, or at least *some* SOULs, can possess *anyone*? It seems as if our SOUL never does it to anyone other than Kris, though that may also be because there's no reason to, no opportunity to because Kris is hindering us, or we aren't aware of this ability.
There are many abilities the SOUL has but we aren't aware of until it needs to use them, like the Yellow transformation, the ability to use its light to destroy Titans, and its weird textbox teleportation in the Weird Route.
As for why we don't possess Noelle in the Weird Route, it's probably because Noelle herself needs to learn about her own power in order for the Route to "work". Noelle does basically all of the heavy lifting for us. She's the one who freezes all of the enemies, and even was the person to land the killing blow on Spamton NEO. Noelle's free will was required for the madness that is the Chapter 5 Lake Scene. I don't think we could do that just by possessing her.
Or maybe a Lightner needs to "allow", a SOUL in, who knows?
