no real 'reason' to disable the Inverter, even when plugged in, because it simply passes thru 120v power from the shore, BUT it also is your backup power should the shore power trip or fail... your fridge would then be without power for that time frame, if you were gone.
I like to always leave the Inverter on, since it really just sits in 'stand by mode' when you're on external power, but ready to take action when that power is lost. For instance, satellite receivers don't like to lose power since they have to reset and reacquire the satellites, and the programming...which can take a while, especially if you are in the middle of a show or movie.
One 'drawback' to leaving the inverter on all the time is that if you DO lose external power, you may not even realize it for a long time, until your AGS kicks on your generator suddenly, or your Inverter actually reaches it's LBCO(Low battery cut off) setting and turns OFF the inverter.
Of course, during the summer, when running the air conditioners, it's a little more obvious when the Inverter has to take over because it does not run them, and they just suddenly cut off.