My splitter is towed either by my ATV, or a trailer in between it & the ATV, into the woods where the trees & rounds are. If I wasn't splitting more than a trailer load, or if I was splitting all of what is in one place in one session, I would leave it hooked up. Except the hitch is usually too low and makes it have a big tilt to it. Otherwise - it is much more stable when hooked to something, and don't have to futz around with the stand & hooking & unhooking. If splitting into a pile, I would definitely try to leave it hooked up, since the wedge is on the end opposite the ball so would pull it ahead once in a while as the splits pile up around the end.
I don't know why they would recommend that, unless it's to try to protect people from themselves & beating up their tow vehicle with splits & rounds & stuff.