The effect of the pattern "blooming" outward at low frequencies is not just that more total bass is picked up from off-axis, but that the bass in a stereo recording tends toward mono, since both mikes are picking up mostly the same low-frequency information in pretty much the same phase and at the same time. That's great for cutting a vinyl LP, but not for modern recording media where you can decorrelate the low frequencies all you want. What you ideally would want, in order to get a feeling of spaciousness in a stereo recording, is exactly the opposite characteristic from that.
Since no real-world microphone has such directional characteristics, the best available choice is mikes that maintain their nominal directional pattern down to the lowest audio frequencies. In and around the cardioid part of the spectrum, single-diaphragm microphones are obviously better than dual-diaphragm microphones in this respect; on the lower end of the spectrum it's the general acoustical design and not the size that matters most. Over the decades, engineers have learned to work with the shortcomings of dual-diaphragm capsules at both ends of the spectrum for spot/solo recording (using isolation and proximity effect, and choosing suitable room acoustics), but two-microphone stereo is a whole other thing, requiring (relative) uniformity of polar patterns across the spectrum.
-- Yes, for front-arriving sound the treble will be "beamier" due to the larger diaphragm. But beware the fallacies of imagining that a microphone has a narrower pickup pattern than a cardioid pattern actually is (it's really more like an omni with a hole in the back), and especially that the first-arrival sound will be what the microphone mainly registers--an illusion that our brains create for our benefit as we use our ears, that we grow up with and habitually take to be the reality of our sonic environment. That second illusion can be especially tenacious.
Most microphones don't know how to pay attention to the main, direct sound component and relegate everything else to being part of the ambience or character of the space the way we humans do unconsciously. I have to say "most" because a few fancy microphones with DSP built in can actually do something like that. But for all other microphones, everything that they receive is effectively "foreground". When you're not recording close-up, and you're in a reverberant space, sound arriving from more or less all angles at once will be the great majority of what reaches a microphone. In the microphone's output signal, the sound will be substantially altered by its particular, peculiar response(s) at all those other angles. That's why off-axis frequency response matters so much for any recording that includes the space that the acoustical events are happening in.
Polar patterns, if you make the effort to read them, reveal that information in a way that most manufacturers don't give out directly. They're like a secret code that only professionals know, or amateurs who've taken the time and trouble to learn how to decode it. That's why I posted my messages above with the table and all. The manufacturers could give you that information directly, but it might undermine their sales of certain products.
-- The original generation of large-diaphragm condenser microphones, back in the 1920s and into the 1930s, were pressure transducers (not cardioids!) with a range only to about 8 kHz, but because of their size they smoothly and regularly rolled off the treble of any sound that arrived off-axis. This includes the Western Electric condensers that launched the era of electrical phonograph recording and motion picture sound almost exactly 100 years ago, as well as Neumann's first capsules from the later 1920s, which were based on the Western Electric design but using metallized plastic diaphragms rather than stainless steel.
That approach gave way in the early 1950s to using a small-diaphragm omni embedded in a sphere (typically 40 mm diameter), such that the diaphragm of the capsule is flush with the surface of the sphere. That's a really useful technique for when you can't (or don't want to) be close to your sound sources; I'm surprised that more people here don't use it. The Neumann M 50 is the best-known historical example--the classic "Decca Tree" microphone. They still had some of those at RCA Studios in Manhattan when I was working there, and it was amazing how they could be placed 20 feet from a group of musicians and convey as much detail as if they were only maybe four or five feet away, while keeping the nice room sound of a big, well-designed studio such as our late, lamented Studio "A".