As a user, I would like arrows (in flowcharts, for example) to maintain a text parameter of its own, so that I can avoid having to move, edit, etc. many separate text boxes that are, in usage, linked to those arrows anyway.
I have many decision diamonds in a flowchart that shows many Yes/No branches. Every time I need to move a diamond to make room for something else, I also have to move the text boxes that I've added near the arrows showing which branch is Yes and which is No. These can even get hidden under other objects if I don't move them first, which more often than not forces me to move them more than once since I don't always know where I'm going to leave the object I want to move.