A screen enclosure would be great if you have a place to store it and could dismantle it easy when not in use. I don't have that kind of available storage space. These pouches scrunch down pretty well in a plastic tub in the garage.
I haven't tried plastic screen, so I can't speak to using it. Steel screen is cheap enough and easy enough to work with.
I have squirrels really fighting to open a number of the pouches this year. They are starting to take it as a challenge. Shredding leaves, chewing the pouches, chewing branches, knocking down pouches, etc. I'm going to up the game a little by adding some tanglefoot around some of the stapled areas. The trees along the block wall are getting pounded right now.