The isostructural transition in the tetragonal phase with a sizable change in the anion height, is realized in heavily H-doped LaFeAsO and (La,P) codoped CaFe₂As₂. In these compounds, the superconductivity with higher T_c (40–50 K) is realized near the isostructural transition. To find the origin of the anion-height instability and the role in realizing the higher-T_c state, we develop the orbital-spin fluctuation theory by including the vertex correction. We analyze LaFeAsO_1−xH_x and find that the non-nematic orbital fluctuations, which induce the anion-height instability, are automatically obtained at x∼0.5, in addition to the conventional nematic orbital fluctuations at x∼0. The non-nematic orbital order triggers the isostructural transition, and its fluctuation would be a key ingredient to realize higher-T_c superconductivity of order 50 K.