The ACA maps have a lot of great features, but I couldn't read one while I'm riding, especially through plastic. The details are too small. If you really plan to use the ACA maps while you ride, you'll probably have to stop to give the map a careful look, which means storing the map in a jersey pocket would work as well as anything.
There are dozens of ways to protect maps or route sheets. If you're not riding in the rain, just clip the map to your brake cables. If you want the map on the side, put a couple of zip ties around your handle bars and clip to those. Or put the map in a zip-lock freezer bag, then clip the bag. I once met a person that used to be in the high school marching band. they used the plastic pouch that protected the music in the rain. Also, there's no biking rule that the computer has to be in the center of the handle bars. They're pretty easy to move.