Even though recreation is necessary for most people to keep a healthy mind and body, it is a sort of weakness.
Since Our Lord was perfect, it seems more plausible to me that he wasted no time at all with recreation. All of his acts were full of merit and beautiful. He did no useless things, or less than perfect things.
Our Lord probably spent all his "free" time praying.
I imagine that the only possibility for Our Lord to engage in some sort of recreation is if it was an opportunity to teach something. Just like when He went to bankets. He was obviously not there because He wanted to enjoy good food. He was there to teach.
I don’t disagree with you, and I had your latter thought in mind, albeit implicitly, when I made my observation. Engaging in recreation, with others, could have given Him a chance to teach them, and to, for lack of a better way to put it, gain credibility with them. No aspect of His earthly life was without purpose.