I like the idea at least "in general". It would be good to discourage the casual editing of already-posted nodes. I fairly often navigate (to a parent node, to a domain where I don't have a cookie, etc.) just to get rid of the edit box because it gets in my way when reading.
Note that we should also mitigate duplicate posting, however. When we have previously had node types with an "edit" link and no textbox, those node types had a higher rate of people not noticing the "edit" link and eventually figuring out that the brower's "Back" button made an textbox appear.