I think this is a combination of things.

1: knot theory is somewhat obscure. it generally only comes up in undergrad in a topology class for a week or two so there aren't a ton of people interested

2. It's 5 cuts on a joining of 2 knots with 6 crossings. it's brute forcable, but not trivially (i.e. you have to code it up and possibly wait a while)

3. for conjectures that feel intuitively true more effort goes into finding the proof than looking for a counterexample that feels unlikely to exist.