I appreciate you being a technical stickler, aaronji.
I agree that the polar pattern is not omni. As you mention, it doesn't look like any generally available cardioid mic I've seen either, though I have not done extensive research.
But on the practical question of what mics will best reproduce the concert experience, I staunchly support omnis unless you are in a situation where you know you will need to reject a roof echo, a balcony reverb, a chatterbox crowd, etc.
Between the ear pickup pattern and the noggin processor, the hearing experience feels omni--like that polar pattern and its mirror image (from the other ear) superimposed. We merge the channels in our heads to provide the illusion of a stable 360-degree sound field with spatial imaging.
As you and gutbucket have pointed out, microphones just aren't that clever.
I was at a concert last night, swiveling my head to look across a big stage and occasionally bopping along--omnis in a more fixed position on the shirt collar--and I realized that if I had had ear-mounted cardioids, the recording would have been a very seasick thing. Maybe XY or ORTF cardioids stably mounted in a sweet spot would be good too, would eliminate that backless void I hear (or don't hear) in front-facing cardioid recordings. Never tried it. But in the rough-and-tumble of concert recording, I'd always go for omnis as the first choice.