Well--the thing is, a microphone's polar pattern is three-dimensional, and cardioid is quite a broad pattern all around--not just in the horizontal plane. A microphone with a narrower pickup pattern is narrower all around, not just in the horizontal plane.
Yes, a supercardioid/hypercardioid has a rear lobe BUT it is markedly less sensitive than the main, front lobe (by >11 dB for a true supercardioid, 6 dB for a true hypercardioid, and something in between for microphones whose patterns are in between), and once again the rear lobe is also narrower in both the vertical and horizontal plane than the main, front lobe is. So all in all, a supercardioid/hypercardioid will pick up distinctly less room sound, as compared to on-axis sound, than a cardioid--despite the presence of the rear lobe.
--best regards
P.S.: The attached composite shows two nice pseudo-three-dimensional polar graphs as published by Beyer. This may help to visualize the situation.