There is a conflict between the assignment setting for submission attempts, and the new quiz setting related to allowing multiple attempts.
The assignment setting defaults to unlimited attempts and changing this to limited does not appear to impact student access to the quiz. As a teacher I quickly learned to ignore that setting and instead rely on the settings within new quizzes, because those actually work as expected.
The problem is that students still see the assignment settings when they access the quiz. As a result a student just ignored my carefully typed instructions that the exam allows only one timed attempt, and spent the entire hour looking at various questions without responding to a single one. Then complained that he thought he had unlimited attempts because the assignment settings said so.
The assignment settings either need to sync the number of submission attempts allowed to new quizzes, and display everything that students see there, or simply hide from students everything about the number of attempts allowed, so that the only way to see that is within the quiz. (Since it has no obvious function, submission attempts could be removed from instructor view of assignment settings as well, but that is not as important.)
This idea has been developed and deployed to Canvas