Banica–Bichon's maximality conjecture for classical permutation groups

Let $S_N$ be the classical permutation group and $S_N^+$ Wang's quantum permutation group, with $S_N\leq S_N^+$ denoting the inclusion as a quantum subgroup. The Maximality Conjecture. The quantum subgroup $S_N\leq S_N^+$ is maximal at all $N$. This conjecture extends the known result for $N=4$ and asks whether the classical permutation group is maximal inside the quantum permutation group for every parameter $N$; the supplied source gives no resolution beyond the stated small-parameter progress.