Zones of Control are also fairly slow in processing and can greatly lengthen turn times. Furthermore, I don't think that being under threat of being fired upon means you shouldn't be able to move at all - it means you'll be fired upon when you do. I'd prefer to change ZoC to that than to make it an absolute invisible barrier. These are the reasons to turn off the option but I also admit it makes for more interesting strategic decisionmaking if it's on so it's a tossup to me.
ZOC's exist around forts when manned but they also exist around cities when the city has a city that generates a zone of control.
Fixed Borders allows units to claim plots and as far as borders fluctuating, I'm not sure how that works now. In a time I took a big break a lot was reworked there and I can't say I fully understand all the rules established for it then. Without it, you are working with culture rules that pretty much play the same through the whole game and more similar to vanilla.