The time invested is negligible. Having the data improves error trapping and adjustment results, and prevents the head of the LS in charge from exploding (if your into that sort of thing)...
Even in the most pure planimetric survey I want my measurements to reflect the existing ground and if I do something naughty like wing a corner in on a twenty foot rod, I want that part of the story told as well.
@thebionicman I think this was what I was really trying to wrap my head around. For example, setting up on a known point and sighting a retro target, the instrument is never going to be exactly on the target. Plus with distance errors...
I did some testing in AutoCAD and figured out that there's enough 'knowns' for the instrument to do the math and figure out where it is. It would take somewhat of a perfect storm, for example, having the angles sighted a bit off, and being out of plumb just enough so that if the total station still measures the right distance and angles, it's location can easily be 0.01' off in either direction along with being who knows how many minutes out with the angle. I know for a fact that this happens in real life because I've seen bad surveys where you can visually see that the surveyor's setup was rotated.
My assumption was that having some redundancy within the 'known' values would provide a means to which the instrument can adjust the error out. Not knowing the height to a known point means it solely relies on the distance and angles to the backsight.