We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
With all of the other things we do to stay fit, sturdy, nimble, and generally functional, is there any need to do specific core exercises?
Yes and no.
But first, let's clear up some common misconceptions. First, "core" is not just abs. Consider "core" to include all of the muscles that exist like a column wrapped around your body from just below your chest down to your hips. Back muscles and oblique muscles are just as much "core" as abs. "Core" is what holds you up, and stabilizes your physique for doing most everything else you do. Muscle pedestals on the sides, front, and back. Otherwise, we would collapse. You can see collapsed cores in nursing homes.
Second, we'll assert that sit-ups and crunches are a waste of time. These are not balanced core stressors and, contrary to popular belief, will neither burn belly fat nor build a 6-pack (a 6-pack comes from low body fat, and is more about vanity and sex-appeal than fitness. If you are a youthful athlete, or a male model, go for it).
What are the best core exertions? Probably deadlifts and barbell squats. The demands on core for stabilization for those is heavy, even if not noticed while executing them.
Fitness-oriented people often fit in accessory core exercises to help their deadlifts and squat performance, for posture, and to sturdify (?) all other exertions we undertake. What are the two best uses of precious time?
Planks and wheel-rollers are. They do not take up much time to do twice weekly, either as calis or as a side dish to a weight session. If you're on the floor anyway doing mountain climbers or pushups, you can superset 3 sets of 30-45-second elbow planks with 10-20 roller rep sets. Planks are the gold standard but rollers are second. To make planks tougher, put a sandbag on your back.
Correct plank form is FLAT. No sag, no arch. For correct roller wheel form, this youtube:
Saying a 6-pack comes from low body fat is like saying a Kenyan marathon runner has bulging biceps. Low body fat merely reveals the underlying musculature more clearly, but it doesn't build the musculature needed to say you have bulging biceps or a 6-pack. Indeed, the exercise DO build a 6-pack while the low body fat reveals it.
I am the only person in our local gym who does front levers, dragon flags, skin the cat's, etc. so I would say (and a trainer told me) I have the strongest core in the gym. So it takes a lot to make my abs sore the next day, but the one exercise I have been doing lately that I can feel the next day is swinging heavy kettle bells from between my legs up to eye level. That is a workout that leaves me gasping for breath and a bit sore for a day or two. BTW I am 69 years old.