The main question would be this: Why would you turn the projector off when you are switching inputs? This is not normal behavior at all and offers no value. Since it is typically believed that the initial startup of the lamp is one of the biggest killers of lamp life, you most DEFINITELY want to keep it to a minimum. It is believed that it is better to leave a projector on for about 20-30 minutes instead of turning it off for 20-30 minutes then turning it back on! That is (about) the loss of life that happens everytime you cycle the power on a projector.
Now, as for why - I can't really say, but these are lamps similar to what you see in parking lots - the big bright white or yellow ones that light the parking lot. You know when they flicker and go out... then take 5 minutes to come back on again? Same type of lamp. It isn't like a normal halogen or incandesent lamp which only takes a second or two to come back on at all.
Other TVs DO take that long - if your other TV is a projection DLP, LCD, or LCoS display. Regular CRTs don't take this long, but they use a completely different technology. Likewise, LCD and plasma flat panel displays don't use the same lamp technology that you are using.
Bottom line: Don't turn the projector off unless you are willing to wait out a full power cycle when you do it and are ready for the loss of lamp life that comes along with the power cycle.