For me, like for many others here, the way it currently works is fine:
- Make the sections short enough so that they fit more or less on one screen.
- Then the checklist is complete once all items are green.
- A non-mandatory flow it critical to remain flexibility (as already well explained by others).
If you do enforce a mandatory flow, as Mario suggests, then the correct way of implementing it would be to offer "Defer" as an alternative to "Check". For example: Swipe right to defer. Deferred items then show orange, instead of white or green. And then something like an counter of deferred items at the end of that section, which directs to the deferred items that still need to be dealt with.