Given flutter can call down to iOS with plugins, and given that the apps are native, apparently, is it not possible to natively use the actual iOS widgets instead of reimplementing them?
For widgets it's not just calling to iOS that matters, but being able to render the widgets as part of the painting process, which Fluter does as a completely separate process from how iOS renders. So to integrate it, you'd need something involving compositing native views properly and yet propagating touch events to them, or rendering native views on top but doing the right masking, or ...