One of my favorite features on the 880 is the top left "activity" button.
Let's say you are watching a program from a satco. Then you want to shift to watching a DVD. If you press the "activity" button, you get the main screen, and can select DVD. The satellite receiver goes off, the DVD player goes on. The TV stays on. The Harmony 880 remembers that the TV is already on, and does not try to turn it off and back on again, as some remotes do.
I have a bulb based RPTV. It must have at least a 90 second cool down cycle, and then takes a bit to come back on. Cycling power shortens bulb life, especially if you turn it back on hot. I'm sure this is a good feature for all TVs.