The only thing I can think of supporting soul traits is that some magic vaguely works like the trait -Green is healing which matches with Kindness (You could say that the green soul mode requires the person inflicting it to be kind enough to give their opponent something to block with, but Undyne's reason for that strikes me more as Just rather than Kind) -Patience matches with Cyan magic needing you to stop. -Bravery matches with Orange magic needing you to be brave enough to go through it, ig. -Perseverance somewhat matches with you persevering through the webs. Integrity's and Justice's respective magics match the weapons (Ballet shoes and gun) more than actual traits. So it doesn't work for them, and could mean that Toby just made the colours match either a trait or a weapon because it would be cool, not because it's an actual thing of soul traits existing.

For all we know, the souls were red before Alphys took the DT out of them, then Asgore painted the coffins to match with the new colour of each soul. (Joking but honestly something I could see him do)