I also leave mine on, but hardly use it... it's as someone said up there just in case I need to use two hands!!! (and I have the strap I mind as well just leave it on there... it's not like it adds more weight to the bag or anything )
I leave it on just because I actually use it sometimes too. I throw it over the shoulder messenger-style & keep my hands free. It's quite functional IMHO. But it's cute w/o it too