My zero tool almost never comes out. I set it this way so that, when changing jobs, if the tools are the same - and they frequently are - I just touch the zero tool to the part and off I go. Very fast and safe.
I gotcha, that's why I make my chuck face zero as described above, then I can measure my stickout with calipers and don't even need to put a tool to it, just put the value from the calipers at the top of my program under VZSHZ value.
On the other hand, you could touch off any tool in the machine and CAL at the value in the tool offset for that tool to get the same result.