Four reasons why "hypercardioids" and "supercardioids"--most microphones which claim to be either one are actually somewhere in between--give you less bass than, say, most general-purpose cardioids or (especially) omnis:
(1) Starting with the simplest: Many manufacturers assume that the main application for these microphones (and thus the biggest market) will be speech pickup in unfavorable acoustical surroundings, so they deliberately roll off the low end of the frequency spectrum.
(2) Maybe even simpler: Good-sounding, highly directional microphones are much more difficult to manufacture than good less-directional or non-directional microphones; specifically, for now at least they're still beyond the capabilities of the high-volume, low-cost Chinese factories. By "good" I especially mean "having smooth, natural-sounding frequency response, and maintaining the same frequency response off-axis as on-axis as far as physically possible" although low distortion, low noise, consistency between samples and high reliability are important, too, of course.
(3) Highly directional microphones have a high degree of velocity (pressure gradient) sensitivity relative to their pressure sensitivity, and the physical force generated by the pressure gradient (the force that moves the diaphragm of a condenser microphone) inherently rolls off at low frequencies. In other words there's an inherent tradeoff between overall sensitivity and extended low-frequency response.
(4) The most complicated, but it's pretty important subjectively: In any enclosed space with rigid boundaries (floor, ceiling, walls), an acoustical phenomenon called "standing waves" causes resonant frequencies to be reinforced depending on the exact dimensions and shape of that space. Not only is the amplitude increased but the "hangover" time of sounds at those frequencies will increase considerably. This phenomenon is most noticeable at low frequencies if the space is large enough and the boundaries rigid enough. If there's a lot of low-frequency stimulus in a moderate- to large-sized room, much of the low frequency sound energy that listeners experience in that room will be the energy from standing waves. However, standing waves occur along particular directional axes, and highly directional microphones tend to reject sound energy which arrives along any axis other than the one containing their own 0-degree direction. So they simply don't pick up the majority of the energy that is due to standing waves.
(5) (which just occurred to me while I was writing this): Most manufacturers, including the ones who are sincerely trying to publish accurate and reliable frequency response graphs, "correct" their published frequency response curves so that they show how the microphone would respond to sound at a distance of one meter. At one meter, proximity effect (which boosts the low- and low-mid frequency response) still has some effect for cardioids, and even more of an effect with supercardioids, hypercardioids and figure-8s. This isn't quite kosher. but almost everybody does it--and the one well-known company that doesn't use a one meter effective measuring distance "corrects" its published curves to an even _shorter_ measuring distance, so that their directional microphones look as if they have even better low-frequency response relative to other brands.
Anyway, given that, if you had a hypothetical company whose published frequency response graphs all looked flat at low frequencies, in actual fact, to the extent that proximity effect was involved in those graphs, then the closer you'd get to the figure-8 (= pure velocity) end of the directional spectrum, there would be less and less actual low-frequency pickup for distant and semi-distant sound sources.
--best regards