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John Hudson The formatting characters should not be displayed at all times. This is an option in apps, and the default is usually for them to be off. In MS Word, for example, this is an option that you can toggle in the Options / Complex Scripts panel.
I think the application is the correct level for this option, since one wouldn't necessarily want to show control characters in all applications, but may have need sometimes to view them in a particular application, perhaps only temporarily. Of course, having a global option that could be over-ridden within individual applications would provide the best of both worlds. A matter for application and system developers, I'm afraid.
I'm loathe to remove the visual control character glyphs from the font, because they can be very useful at times, especially those that affect Hebrew rendering such as ZWJ.