Distribution of gas fraction f_H2 vs. bolometric luminosity L_bol. Galaxies in the simulations are selected to match the observed parameter range in stellar mass and SFR, and to host AGN with L_bol > 10^44.3 erg s⁻¹ and λ_Edd > 0.01. Contours contain 90% of the selected systems and extreme outliers are shown as individual points. The color-coding for the simulations is as follows: EAGLE, TNG, and SIMBA in purple, red, and orange, respectively. Observational points are shown as gray pentagons for KASHz AGN (presented in this work) and gray circles for SUPER AGN from C21, scaled by α_CO = 3.6 M_⊙ (K km s⁻¹ pc²)⁻¹. The black arrow marks the downward shift for α_CO = 0.8 M_⊙ (K km s⁻¹ pc²)⁻¹. The bottom left point shows the mean error bar of the observational sample.