Who are the 'they' in this? The club? No of course not. I'm not suggesting leaving lids on makes the club re-use them, but some customers. If your 'they' is the customer, then I disagree. Yes, there will always be some who throw them away, but there are plenty of people out there who like to reuse the pop bottles - convenient to put squash or water in when popping out to the park, somewhere there isn't a convenient shop etc. They can't do that if the club doesn't let them have the tops, so they are more inclined to throw it away.
I'm guessing you have plastic bottles at home so surely that will meet your reusable purpose. It would be really sad if you were missing out on taking squash to the park just because of a national Premier league policy regarding bottle tops. Worthy of a letter to your MP?
Also, by they, I'm referring to companies that recycle plastics.