Shaving sharp is my minimum for carry, as on my coarsest stone I get my edges to shave. At DMT Coarse you can get a really nice shaving edge with good microteeth for slicing. For toothier edges that are really sharp Tom Krein is king in my experience with his tree topping, free hanging hair cutting 120 grit edges. My OCD makes me get at least free hanging hair cutting (usually around Spyderco Medium), or most likely hair whittling sharpness (varies from Spyderco Medium to UF depending on the knife and my caffiene level) on my EDC's (I carry more than one), and when they fail to shave I resharpen them. Most of my knives will still cut well enough to do the job at the point I deem them too dull, especially my Krein regrinds, but I have so many different folders it gives me a chance to rotate EDC knives and get in more sharpening time (this is the whole hobby vs. tool debate). For use as a tool, if it still does the job and cuts good enough to complete the task then no, of course your knife doesn't "have" to be shaving sharp as long as it makes the cuts you want.
Most of my Kitchen knives get marathon sharpening sessions up to .05 micron lapping film for great bragging edges that scare people used to a dull Wustof when they use them. Plus, on my Takeda Gyuto, at 8000 grit the 4 degrees per side edge still looks toothy under magnification, so I feel the compulsion to takes it up to .05 microns. At that sharpness level with such thin geometry it guillotines through food and sticks itself into the cutting board on every cut. That is quite a satisfying feeling.
Mike