After transitioning to new quizzes this semester, I discovered that there is a major flaw in the interaction between new quizzes, the late penalty, and module requirements.
Although a new quiz can be used for practice, by setting it to not count towards the grade, it will still appear in the gradebook, which means that any late policy will be applied. When that new quiz is used as a module requirement that students must "score at least," the late penalty can eventually make it impossible for students to meet that minimum score. (If the minimum score in the late policy is applied, then it is not possible to score less than the minimum score, and so there is no point to the module requirement.)
Designing a true practice quiz in new quizzes has already been suggested: https://community.canvaslms.com/t5/Idea-Conversations/New-Quizzes-Practice-quizzes/idc-p/403844#M357...
That may take time to achieve and so I have a faster suggestion to address this in the meantime. Program "score at least" module requirements to use the score from before any late penalties are applied.