Exporting includes formatting as well as field selection—which is why templates are used to define them. So it's not clear how such a thing would be implemented. I suppose a pick list for inserting field names into a template could be added. But that would be of limited use if it could only add one field at a time (i.e., what you would expect a pick list to do). To be useful, it would have to be like the import field lists—with some rather unique options for how it inserts the results into a template. One would be the matching header and field semicolon-delimited lists used in a CSV or list-type template. Another would be caption and field columnar output for other report-type templates. A variation of that would be one that includes appropriate coding for an XML template.
In the absence of such a feature, this is what I've been doing: For CSV exports, I have a master template that includes all standard and custom fields. I either use that and delete the columns I don't want in Excel, or copy the list into a new template and delete the fields I don't want to export. For a report-type, I start by editing a copy of the provided "Sample" template.