Short answer: On.
I did know this guy who asked me one day about a laser boresighter. As I dug into what his needs were, it became obvious that he was taking the scope off the rifle after each trip to the range.
Oh, that's the way you're SUPPOSED to do it. Din't you know?
It turns out he had been removing the whole shebang off the rifle after each trip to the range. I tried to get him to understand.
NOW! having said all that there ARE some mounts that allow removal. Leupold makes a mount and rings that work very well. I've tried it. It works. You can take the scope off the rifle and put it back on and it returns to zero. I have them on my 7600 in 35 Whelen. They work, but they came with the rifle, and I have not removed the scope except once to change it out.
I've seen other arrangements, but in general the scope stays on the rifle. There is just so much trouble to get everything sighted in just right that most folks don't want to risk throwing it off by monkeying with the scope afterwards.
BTW: I had a situation over the fall that kind of fits into this. Angus has been shooting KYHillChick's 30-06 for several years. It fits him well. This is one of Savage's package deals. Anyhow, middle of the afternoon's shoot, I noticed that the rings that had been installed at the factory had come loose. We bagged up the rifle, brought it back home to the bench, and I set about redoing it right with Locktite,etc. We brought it out the next weekend, and we were on the paper with the first shot. I thought that was pretty darn good work. Warning: the scope blew itself up after a year. Don't trust the Savage package rifles. The rifles are fantastic, but get a rifle and a scope and rings and such and do it right.
One other thought, and then I'll leave you. You know a lot of goofs go out to Walmart on the night before The Opener and get a rifle and get the scope mounted by the clerk, and think they're good to go. Right? Most of us "right thinking" folks make fun of these folks for being so ignorant and not taking the gun out to the range and doing proper sighting in. Truth is, if you take most properly bore-sighted rifles and take them up into a treestand and try to shoot a deer inside 50 yards, you're going to come home with venison.
However, if you are inexperienced enough to try this, you're probably not going to limit yourself to 50 yards, you're probably not using proper support for your shots , and you get all worked up before you try to shoot off-hand, so the net of it all is rather chaotic and having a rifle that has only been bore-sighted adds a marginal amount of uncertainty to an otherwise random flinging of metal at a now-desperately fleeing target.