Torsion existence conjecture for non-split links

Let $L$ be a non-split link. Khovanov homology means the integral Khovanov homology of $L$, and $2$-torsion means torsion elements of order $2$.

Torsion existence conjecture. Except for the trivial knot, the Hopf link, and their connected sums, the Khovanov homology of $L$ has $2$-torsion.

The conjecture was motivated by computations of knots and links with bounded crossing number. The supplied text gives no resolution status.