I suggest that the current "Add Field", which is the first button on the left at the top of the attribute table, be replaced simply by the Fields button.

Having the Field button there allows for more flexibility. Currently, if you want to open the Fields view, you have to go to the Top Ribbon, select the Table Ribbon, and then click on Fields.
I often have to modify fields, and I use the Add field button just because its closer, but I don't want to add a field. Having the field button instead would allow the user to open the Field view. If the user needs to add a field, she simply needs to click on the bottom.