Then maybe you all should come up with a compliance plan for this and be the ones to enforce the policy

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A: I think you missed the point we were trying to make, which is that it's a stupid policy to begin with, that shouldn't be enforced. (NOTE: NOOOOOOT that requiring books to be covered is stupid, but that requiring the fancy-schmancy fabric covers is stupid.)
B: Here are some more appropriate compliance plans to get the books protected, which is the only goal you've stated that you are trying to accomplish:
1. As PPs suggested, have a book covering party in class using donated paper bags. (If this is the type of school where lots of kids have fabric covers, I'm quite sure a call for paper bags would be met with plenty.)
2. If covering all books as a class is too much, make kids do it at home. Thos that don't do that can be held in at recess and make them cover their books during that time. Once they are covered, let the kid go play and get some exercise.
3. Call the offending parents and say "Hello Mrs. Soandso, I know it's a busy time of year, but we noticed that little Billy doesn't have his books covered. Can you please make sure to do that by tomorrow?"
4. Take the book away from little Billy until he does bring in the appropriate cover. Any missed school work will be his responsibility to make up. (My least favorite, as it starts hampering learning, but at least it makes some sense.)
The current "compliance plan" doesn't, in fact, do anything to meet the goal. Here is how the scenario likely often plays out.
Mrs. Soandso (forgets/doesn't care/doesn't have time/whatever) and little Billy goes to school without the appropriate cover. He misses recess. Little Billy mentions it to his mom about 8:30 at night when he's getting ready to go to bed. Mom can't do anything about it at that point. Little Billy misses recess #2. Mom has a busy day at work the next day and Little Jane, Billy's sister, has an event, so mom can't do anything about it that night either. Little Bily misses recess #3. All the while the book still isn't covered because the school insists on being stringent and mean and not allowing brown paper bags.