Rationality conjecture for irreducible free plane curves

Let $C\subset\mathbb{P}^2$ be an irreducible plane curve of degree $d\geq 2$, and suppose that $C$ is a free divisor, meaning that its logarithmic vector-field bundle splits as a direct sum of two line bundles. Rationality conjecture. Then $C$ is a rational curve.

The conjecture is motivated by the limited number of known irreducible free divisors, which include several rational cuspidal families and the Cayley sextic; the source does not give a resolution.