Cache is separate from localStorage. Clearing your cache should have no effect on your SC4 keys. (Also, if you're running one of the two standalone versions, your key is stored in a file.)
At least in Firefox, clearing cookies (not an unreasonable thing for users to do once in a while) will also clear localStorage.
That's true. There are limits to what one can do when running in a browser. If you have a better idea for where to store keys, I'm all ears.