I think it comes down to the difficulty of finding such things. The goal is usually to find "enough" invariants that all objects can be distinguished, but we se

I think it comes down to the difficulty of finding such things. The goal is usually to find "enough" invariants that all objects can be distinguished, but we settle for just whatever invariants we can happen to find. Finding an invariant is pretty easy: it's straight-forward to show that something is invariant under a certain transformation since you just apply a transformation (in this case, usually a homotopy or similar) and see what it can do to the invariant. For knot theory, you can often check just what it does under the Reidemeister moves, giving you just a couple things to check. How would you go about showing that something is a dinvariant? You would need to take two objects that are distinct and show that their dinvariants are distinct. I.e. use the fact that a homotopy between the two knots does not exist. This is much more difficult, though it does get done. In particular, it's done whenever we have a complete classification of all objects of a certain type (say orientable surfaces, classified by the single invariant (and also dinvariant) their genus). Though generally here we would be actually approaching this from an invariant perspective but just showing that once you have enough invariants, they collectively become a dinvariant.