We are one of those that remove them except for when dousing the main. This allows us to use a standard sail cover, and gets them off the sail and avoids any chafe and wear that might occur there.
You do need to be fully luffing or the jacks can hang up the sail, but that is worst with partial battens, and less of an issue with full battens.
The bottom half of our
lazyjack system is made of shock cords, so we can store them to a handrail when no in use. This also takes away any issues with overtensioning the jacks with the mainsheet if you leave them in place while sailing.
The main reason we have them is to protect the price Lexan dodger windows, which scratch amazingly easily.