In chrome, for now, double clicking the string select both the field key and the field number beside it, making the copy/paste quiet cumbersome
Screenshot here of the selected area after double-clicking the string :
https://www.dropbox.com/s/0gplzg7jrpckqgn/Capture%20d%27%C3%A9cran%202015-03-03%2016.47.13.png?dl=0
Cheers
This has crossed my mind too. The CSS solution would be:
.acf-field-object .handle .acf-icon {
-webkit-user-select: none;
-khtml-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}