Document preservation

Answer:
No, ISO 9001:2015 does not mandate the use of plastic covers.
I believe that that idea came to life because of ISO 9001:2015 clause 7.5.3.2 b) about preservation.

If preservation is an issue because the flyer, for example, will be posted on a place where sun and rain can deteriorate its legibility, perhaps the plastic cover makes sense as protection. But it is not mandatory nor needed everywhere.

You can find more information about document control here:
The following material will provide you more information on ISO 9001:
ISO 9001 – Some Tips to make Document Control more useful for your QMS - https://advisera.com/9001academy/blog/2014/05/20/tips-make-document-control-useful-qms/
You can enroll for free at ISO 9001:2015 Internal Auditor Course - https://advisera.com/training/iso-9001-internal-auditor-course/
ISO 9001 – How to set up doc ument approval/withdrawal within your QMS based on ISO 9001:2015 - https://advisera.com/9001academy/blog/2016/04/12/how-to-set-up-document-approvalwithdrawal-within-your-qms-based-on-iso-90012015/
Book - Managing ISO Documentation: A Plain English Guide - https://advisera.com/books/managing-iso-documentation-plain-english-guide/