How can I make Word 2013 open in Draft View by default?

Follow the instructions at http://www.gmayor.com/installing_macro.htm to put the following two macros into a module in the Normal.dotm template:

Sub AutoOpen()

    ActiveWindow.View.Draft = True

End Sub

Sub AutoNew()

    ActiveWindow.View.Draft = True

End Sub

The first will run automatically every time you open an existing document, and the second will run when you create a new document.

That one's hidden about as deeply as possible. A lot of the things in the Options dialog are properties of the Options object in VBA, so you can say things like Options.Overtype = False. Controlling the draft font display is not one of those things. :-(

Actually, it's a throwback to Word 2003 and earlier. The Dialogs collection includes a member called Dialogs(wdDialogToolsOptionsView), which refers to a tab of the Options dialog that no longer exists (and of course the Options command isn't on the Tools menu, which doesn't exist). That dialog has an argument named DraftFont, which is a boolean (true/false) value. So this is how you do it:

Sub AutoOpen()

Dim dlg As Dialog

Set dlg = Dialogs(wdDialogToolsOptionsView)

With dlg

    .DraftFont = False

    .Execute

End With

ActiveWindow.View.Draft = True

End Sub

and similarly for AutoNew().

By the way, both your original problem and this one point the the probability that there's something amiss in your Windows registry, because these things should be saved there automatically. This trouble sometimes happens when you have certain third-party add-ins or other programs that interfere with Word's ability to write to the registry. There can also be misconfiguration of the permissions for certain parts of the registry. If you think that working with macros is harrowing, you don't want to know how to troubleshoot the registry. If these two macros solve the problem, leave well enough alone.