Definitely leaving most devices like these on is better than constant on/off. When I got my first computer, I would only turn it on when I used it, which was for maybe a half hour, once or twice a day. After a little while, I started using it a bit more, and eventually I realised it was better and easier to leave it on all day.
With my arcade monitors, however, I don't have them on while I'm doing other things, so any particular one may only be on later in the day/evening. Of course, my main rig I also flash in and out of games and surf and stuff, so it's on for some hours.
As well - as someone else mentioned, I think, above - the constant changing of sync when switching between FE and games is a factor.
Visitor Q I kinda have my eye on that one too!
Those seem kind of a lot for that function, though. I might look on ebay for something similar likely for less.