In Data View, an empty edit cell for a numeric field implies that it has not been edited and hence you cannot write it. The question then is, for a string element with Data View's ASCII edit/display format, does an empty edit cell mean that it has not been edited, or it has been edited but is an empty string? To be consistent with numeric fields, an empty edit field of a string in ASCII format is interpreted as unedited.
As BobO stated, switching a Data View's string element format to Quoted format, the edit field state can now be distinguishable. In Quoted format, an empty edit cell is in an unedited state (and cannot be written), but an edited cell that contains two double quotes "" is an empty string (and can be written as an empty string).