To be fair, there are a couple of other, possibly less desirable, factors to consider.
Screened enclosures are not necessarily maintenance free. Over time, an enclosure may develop mold or mildew which would need to be pressure washed. While the amount of time this would take is far less than cleaning leaves every day, it is something to take into account.
The other, which does not happen that often, is when a screen gets torn or damaged. An example may be if a heavy branch were to break free from a large tree and fell into the screen. Not an easy fix when over the pool, but not an impossible task, either.
At Hive Outdoor Living we will help you Create Your Own Paradise, with or without a screened enclosure. The choice is entirely up to you. And, if you decide to install an enclosure, there are different styles from which to choose.