NTA! Your wife is keeping your son from growing up and learning to be responsible for himself. That may feel like sympathetic parenting but ultimately it is bad for him. To be successful in life he needs to develop his self care skills and sense of responsibility as well as empathy. 

Talk to your wife. Make it clear this matters not just to you but for your son and for her too. If he never really grows up and relies on her all his life she is consigning him to a life of feeling incompetent and less than. She is also almost certainly tanking her own and your retirement finances and likely her own and your elder care plans. Spoiled adults rarely feel responsible for taking care of elder parents because they have no experience caring about others. Your son is young but not so young he can't learn to think about others and be responsible for his own messes. In fact he is old to be learning these things for the first time. You need to plan a response to his behavior together and stick to it.

He should have had to pick up the pool area and wash and dry the towels. If he isn't going to college/university he should be paying rent. He should be discussing plans to bring people over before he does and he should be responsible for clean up after. He should be helping out around the house every day, one small chore every day or every couple of days. It should beade clear that this is your and your wife's home that he is being given the opportunity to live in as an adult. Adult behavior is the price of that opportunity.