Ensuring integrity definitely requires in person proctored exam centers. It does not require hand written exams.

Hand written exams are either very labor intensive to grade or are confined to multiple choice, so either inflationary to cost of education or inauthentic / inaccurate representation of most knowledge and skills.

The best answer, which enables authentic meaningful high integrity assessment that is also unit cost efficient is to have testing center facilities with institution supplied devices and well trained proctors.

This way instructors can assess students in ways that are relevant and authentic to the subject matter while ensuring the assessments are accurate, consistent, fair and actually reflect the students abilities.