While I really haven't even considered closing in my lanai, I'll make this observation!
Most of the enclosed lanais that I see as I travel about TV back to a major street and, therefore, are enclosed for quietness, I assume.
My own back lanai opens to a quiet space between neighbors. I wouldn't even consider closing it in, as it is my favorite place to enjoy my morning coffee and newspaper, at least on those mornings when the temperature is comfortable and outside stresses are minimal!
SWR