I was going through some help material on icons to answer another when I found something on Mechanism icons ~ the animation display icons for connections, servos, force, etc ~ that show up on the part. This led me to wonder if I hadn't answered the 'wrong' question, since there does seem to be a second interpretation. I can easily see how turning off those 'icons' with 'View>Display Settings>Mechanism Display' could speed up screen resets since they are part of the display.
Unfortunately, I can only confirm your failure to find any way to permanently change these settings. Pro/e is not a Windows program, simply making interface changes is not 'remembered' by Windows, or by Pro/e, for that matter. The only way Pro/e remembers is by creating and later referencing a settings file of some kind. When you can create such a file, there is a menu option somewhere, sometimes at the top of the setup screen, that says 'File' and will allow you to save a file with those options settings. Then there is some confi.pro option that calls out that file. But, as you probably noticed, there is no such menu in the imaginatively titled 'Display Entities' window. The place then to look would be config.pro and there are a bunch of sim_display_* type options but changing them does not turn off the motion setup symbols in mechanisms. Also checked out layers as there are an enormous number of new things that can be searched on and used to place things (generally features) on layers. No luck there, either.
Sorry, looks like we're sol, better hang on to that map key. Maybe this is one of those things that drives Pro/TOOLKIT sales. Anyone know if PTK lets you access settings like this and change defaults to which Pro/e provides no access or way to permanently change?