Removing one's property from a deck chair after 10-15 minutes in practice is inconsiderate. Many people go into the pool for more than said time to enjoy the water and relax, swim laps, or enjoy their families. Many, many people also go into the hot tub and happily enjoy this poolside activity for 20 minutes or more. There is nothing wrong with enjoying these activities beyond 15 minutes--in fact it's quite normal and routine. When people pay to enjoy their time at the pool, they should not have to worry about the pool police or anyone else claiming their belongings which could be quite valuable.
Of course, there are people who abuse this, but your proposed solution is neither reasonable or practicle. This proposal could easily lead to hundreds of people being improperly inconvenienced and disturbed. It would be a daily nightmare for the customers and the staff--a daily nightmare.
A 40 minute trial is more reasonable and if it turns out that what is gained is not worth the confusion and bad will, then it may be best to work out another plan or revert back to what is current as a perfect solution may not be possible--in other words, a utilitarian decision for all affected parties.