It may be possible that you can forgo situps and such and still do fine. I've been a strict cycling monoathlete for over 50 of my nearly 70 years. I've never done stretching, yoga, weights, running, etc., etc. The state of my neglected "core" (whatever that is) has never suffered as a consequence in any way that I can detect. The last time I saw a doctor, about 7 years ago or thereabouts, he told me that I'm healthier than 99.999 percent of people my age.

Based on my experience, I think that cycling (at least, doing 10 hours or more per week at ex-bike-racer training level) is more broadly beneficial than many people believe it to be. (I have wished at times that my arms weren't quite so pipe-stem-like, but not enough to do anything about it.)