- For "the idea" and "the start", your usage is correct and changing it would be incorrect. - I don't think the explanation of "all cases" vs "all the cases" f

- For "the idea" and "the start", your usage is correct and changing it would be incorrect. - I don't think the explanation of "all cases" vs "all the cases" fully works. I agree with other commenters that in this example, either phrase might be used. (Whether the sentences comes after a point-by-point discussion or before.) To me, the version without the has a less natural feeling. You might describe it as more formal, or more stilted, or more abrupt, but the main point is that it's going to be somewhat dispreferred. There isn't necessarily a reason for the preference to tilt one way or the other.