When every irreducible character is a constituent of a primitive permutation character

Wall's theorem claims that a finite solvable group $G$ has at most $|G|-1$ maximal subgroups. A recent proof of the theorem uses a partial correspondence between maximal subgroups and irreducible characters. In this note, we characterise the extreme case of that proof: when is it true that for every irreducible character $\chi$ there exists a maximal subgroup $M<G$ such that $\chi_M$ has a principal constituent?